Mathematical Researches

fa نگاشتهای نرم-جمعی در قدرمطلق پوشا بین جبرهای حقیقی لیپشیتس با برگشت لیپشیتس Surjective norm-additive in modulus maps between real Lipschitz algebras with Lipschitz involution آنالیز Anal علمی پژوهشی بنیادی S چکیده    فرض کنیم <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> و <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> فضاهای متریک فشرده ، <m:omath><m:r>τ</m:r></m:omath> یک برگشت لیپشیتس بر <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> و <m:omath><m:r> </m:r><m:r>η </m:r></m:omath>یک برگشت لیپشیتس بر <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> باشند. همچنین فرض کنیم به ازای هر <m:omath><m:r> </m:r><m:r>x</m:r><m:r>∈</m:r><m:r>X</m:r></m:omath>؛ <m:omath><m:d><m:e><m:r> </m:r></m:e></m:d></m:omath><img alt="" src="data:image/png;base64,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" style="width:78px; height:17px" >،<img alt="" src="data:image/png;base64,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" style="width:92px; height:17px" > ، به ازای هر <m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr> </m:r><m:r>y</m:r><m:r>∈</m:r><m:r>Y</m:r></m:omath>؛ <img alt="" src="data:image/png;base64,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" style="width:83px; height:17px" > و<img alt="" src="data:image/png;base64,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" style="width:90px; height:18px" >، <m:omath><m:r>A</m:r></m:omath> یک زیرجبر حقیقی<img alt="" src="data:image/png;base64,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" style="width:44px; height:17px" > باشد که شامل <m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Lip</m:r><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>&sbquo; </m:r><m:r>τ</m:r><m:r>)</m:r></m:omath> است و <m:omath><m:r>B</m:r></m:omath> یک زیرجبر حقیقی<m:r>C</m:r><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r> </m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>η</m:r><m:r>)</m:r> <img alt="" src="data:image/png;base64,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" style="width:43px; height:18px" >  باشد که شامل <m:omath><m:r>)</m:r></m:omath><img alt="" src="data:image/png;base64,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" style="width:66px; height:18px" > است. ثابت میکنیم اگر <m:omath><m:r>T</m:r><m:r>:</m:r><m:r>A</m:r><m:r>→</m:r><m:r>B</m:r></m:omath> یک نگاشت پوشای <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAM9JREFUOE/Nki0SgzAQhQNnSREdTkBPAJgqbFyQYDhFTSx1tVVV4QRwggwiy13SBWaalB+B47nNvt3M+xLPGEMOyj/oH+0nm2nyvPml8EmTe2s5jo3AyA0EFwAi4tIpIgFYYS9yh6bTFQMakB5omoWzlRbtOCr5tNC0Bd3gNmiFViDXFLvbcu95JhiMkVelb59gXGgV13XsMLANLjFZ2LNL2Sk97D/2fx5a3InKQPKufFi2y+klg7jK3kxXIFSyzxuR2D0TSnsws1rJO/G//gKhmHNuCrdGOgAAAABJRU5ErkJggg==" style="width:17px; height:17px" >-همگن نرم-جمعی در قدرمطلق باشد ، آنگاه دوسویی یکتای  <m:omath><m:r> </m:r></m:omath><img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAARCAIAAADi2T3bAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAVVJREFUSEvdVssBgjAMBWdRT04AE7hIuTpKXaZs4BKwCzZpWlpoSUE8QE5a0pf38oNyGIbiyHY5MnngfiYB/bsuwZp2oSrWqX734NU2eIX+7VFNQjQsKNoivJ4BZ52sCqH8k9hv8KpkZx4pkXGDQ5w815gWlIcv8DJwCs0xTElAofoeL3glfUoLEMiB1wJAsOGrLxDx4GzMt+OCSZK/0O+ksFWMKMQqVznZKTD7lMZRwHgaNIwXyqvzhhTbsqfrl9fO+h3AVSDFbo0A8E1ZoleVgAJnzJeZgXkEtrXXCEgkIT2hSqCunBhGAFmsbHwLmXmRmOXF2Q90LAwo0aflgpDelpmE8ARYpzD5UQEOT6OBUbH5pceOCyG7pWI6r3rqOG7DBCBBBVj4hIPNZs7a2xrDW5EBxJk+Jfb4EPgjxvX++Lxu8w+dzSWNv37Y7bVnPMA6fAt9AakagVtx4rBfAAAAAElFTkSuQmCC" style="width:64px; height:17px" > وجود دارد به طوریکه به ازای هر<img alt="" src="data:image/png;base64,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" style="width:69px; height:22px" >  و<img alt="" src="data:image/png;base64,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" style="width:57px; height:17px" > ؛ <img alt="" src="data:image/png;base64,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" style="width:106px; height:17px" >. با استفاده از این موضوع نشان میدهیم اگر <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> و <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> فضاهای متریک فشرده باشند و <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJYAAAARCAIAAACw1sLVAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAyFJREFUWEftWDuS4jAQ1cxZgIDiBJ4TAAkRKZkcQrIZIQcwIa7agHQikrFPMJyAIhh8F7bb+iBLbUtmgC2qUGTkVuu9/pu38/nMXuuZLfD+zOBf2NECLxc+fRy8XPhy4dNb4OkJvLNi/fFmr491QTDLYyFXfYvnaflA42gFCkmcM40Knz1LHENBBBhwwKdQKLob079CubSZvKoNbJvmKYmi5ARzacaZfuAZbBALhJn9DvfEwSuWddjUr/H41cIxjarFsSbFd2VawQg/HJv6KRsqmJK+YD4lvM4jFDH/dbUSOnwuEhn3xpGrTh0Sbwit7THelWk1Uq+Mf01TuxDcauUXkV4uMdxRUVQ+AyCMK1w+bKSt0R2ZkVX11lfXcG5BDzZ/q2C9JVOFMCzaFFHLoEqJciFRf4JcKCqwcr5J01sgaiwdVglRuwwRMvh84SMjo9bb5IvbMS3VJ6qHNRWJixkdSDIA5EdF8XOIpuNOpdF35t/n73l1zz8JgDs3QxQbTjg7/BTWtORp2yC9Y3x/PHkuyndplGxLcAi937XlHRVqQqlObt3FnqWjK6exXzDt9AYsXRyXPvsW61WqrqFMgjSFC4uvz/2g19pbAQ5lnfkygcqI7TWDh/6OHHaFpjyese1mM+HprnkQRQ/KiAPozA4+CtdwQ8Z6mVg+Q4bwZK2Yij7zp4z1pnU67vlESsEzEavy3xn0oPvW97UA76mcgswT/tilzAmLbm9SFymgbtUvEwvyN10pTyOK+tTNY8gjuCWPLRmSrG0szPnJWRSNpnVjpsI4TtUjmBoVJo9HKV/aRbGkWU5wJX67fTi9ULdVRRdPyE3RDZWqij5MvvKKKEm4OTIZzVxoEQikEgmH7lZ6lMnM9utrcMGD6R2ZGlayDE7OilEknEN8eNjjTDC7RkF6CBCFFJu3FScBo6M7q3iRho15XjXNAg9h2khe03zcf6Tj8ZRxPljMLs2wM98mh1HjhAMtzF/ozCJYrGefUzHo/K91K6ZQRnUjdHvAheYvo9E8rspo5ftS11bYrRRdfdL4PvglmNtp8gB5CNPaamLR/AdtijWJXgaO2QAAAABJRU5ErkJggg==" style="width:150px; height:17px" > یک نگاشت پوشای <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAM9JREFUOE/Nki0SgzAQhQNnSREdTkBPAJgqbFyQYDhFTSx1tVVV4QRwggwiy13SBWaalB+B47nNvt3M+xLPGEMOyj/oH+0nm2nyvPml8EmTe2s5jo3AyA0EFwAi4tIpIgFYYS9yh6bTFQMakB5omoWzlRbtOCr5tNC0Bd3gNmiFViDXFLvbcu95JhiMkVelb59gXGgV13XsMLANLjFZ2LNL2Sk97D/2fx5a3InKQPKufFi2y+klg7jK3kxXIFSyzxuR2D0TSnsws1rJO/G//gKhmHNuCrdGOgAAAABJRU5ErkJggg==" style="width:17px; height:17px" >-همگن نرم-جمعی در قدرمطلق باشد ، آنگاه یک همسانریختی لیپشیتس <m:omath><m:r>φ</m:r></m:omath> از <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> به <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> یافت می شود به طوری که به ازای هر<img alt="" src="data:image/png;base64,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" style="width:82px; height:17px" > و <m:omath><m:r>y</m:r><m:r>∈</m:r><m:r>Y</m:r></m:omath>؛ <img alt="" src="data:image/png;base64,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" style="width:127px; height:17px" >.   Let <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> and <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> be compact metric spaces&sbquo; <m:omath><m:r>τ</m:r></m:omath> be a Lipschitz involution on <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>)</m:r></m:omath> and <m:omath><m:r>η</m:r></m:omath> be Lipschitz involution on <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath>. Suppose that <img alt="" src="data:image/png;base64,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" style="width:78px; height:17px" > for all <m:omath><m:r>x</m:r><m:r>∈</m:r><m:r>X</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>&sbquo;</m:r></m:omath><img alt="" src="data:image/png;base64,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" style="width:94px; height:17px" ><img alt="" src="data:image/png;base64,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" style="width:80px; height:19px" > for all <m:omath><m:r>y</m:r><m:r>∈</m:r><m:r>Y</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>&sbquo;</m:r></m:omath> <img alt="" src="data:image/png;base64,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" style="width:90px; height:20px" >, A is a real subalgebra of <m:omath><m:r>C</m:r><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>τ</m:r><m:r>)</m:r></m:omath> which contains <m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Lip(</m:r><m:r>X</m:r><m:r>&sbquo; </m:r><m:r>d</m:r><m:r>&sbquo; </m:r><m:r>τ</m:r><m:r>)</m:r></m:omath> and B is a real subalgebra of <m:omath><m:r>C</m:r><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>η</m:r><m:r>)</m:r></m:omath> which contains <m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Lip</m:r><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo; </m:r><m:r>ρ</m:r><m:r>&sbquo; </m:r><m:r>η</m:r><m:r>)</m:r></m:omath>. We prove that if <m:omath><m:r>T</m:r><m:r>:</m:r><m:r>A</m:r><m:r>→</m:r><m:r>B</m:r></m:omath> is a surjetive <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAANdJREFUOE9j/P//PwOJgIlE9SDlROrZnp6+HW46E8P2dEZMgKQCi0OA/rk9IW3C7dsTrNK2IXGsJtwG8oByVsiawKIYblNRY7h2W8U7TAeiVCX/KEjrtjSwgf+P5qtg8c+dW1eASm8zaHkDZbEDZHtmeQE9Fs+wsPSW9QY1kIEI4DlzpidSGCAk0rYBfaZzLV614NiVW3dwRwKqf1TyAxiuhN3elnasoBsRtui60cPAszRsVfyt0tsTrnjhDm9gkCDMAQclQgASVhiAcXClN5RgIDKNUqwHAERic278YfbvAAAAAElFTkSuQmCC" style="width:17px; height:17px" >-homogenous norm-additive in modulus map then there exists a unique bijection <img alt="" src="data:image/png;base64,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" style="width:60px; height:20px" > such that <img alt="" src="data:image/png;base64,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" style="width:106px; height:17px" > for all <m:omath><m:r>f</m:r><m:r>∈</m:r><m:r>A</m:r></m:omath> &sbquo; <m:omath><m:r>y</m:r><m:r>∈</m:r><m:r>Y</m:r></m:omath> and <img alt="" src="data:image/png;base64,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" style="width:57px; height:19px" >. Applying this fact&sbquo; we show that if  <m:omath><m:r>(</m:r><m:r>X</m:r><m:r>&sbquo;</m:r><m:r>d</m:r><m:r>)</m:r></m:omath> and <m:omath><m:r>(</m:r><m:r>Y</m:r><m:r>&sbquo;</m:r><m:r>ρ</m:r><m:r>)</m:r></m:omath> are compact metric spaces and <img alt="" src="data:image/png;base64,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" style="width:150px; height:17px" > is a surjective <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAANdJREFUOE9j/P//PwOJgIlE9SDlROrZnp6+HW46E8P2dEZMgKQCi0OA/rk9IW3C7dsTrNK2IXGsJtwG8oByVsiawKIYblNRY7h2W8U7TAeiVCX/KEjrtjSwgf+P5qtg8c+dW1eASm8zaHkDZbEDZHtmeQE9Fs+wsPSW9QY1kIEI4DlzpidSGCAk0rYBfaZzLV614NiVW3dwRwKqf1TyAxiuhN3elnasoBsRtui60cPAszRsVfyt0tsTrnjhDm9gkCDMAQclQgASVhiAcXClN5RgIDKNUqwHAERic278YfbvAAAAAElFTkSuQmCC" style="width:17px; height:17px" >-homogenous norm-additive in modulus map then there exists a Lipschitz homeomorphism <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAATCAIAAADNvrC6AAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAI5JREFUKFNj/P//PwMOwIRLAig+1OS2pzOmb2dgAFJgYD3xDtATQL/fnmDFkLYNQf/flsZgNeH2fyaGOxPjC3S2zfRkuLN1FcOEUk+kwAApAmmC6/4P0/afASwGMgGqBsSFKAbKQXQgAEgdBIDkwABmNIwPpGFhfefWFSstVdRIgcqB3BjmrYIqx0hm3AIAmVtxQYXS1YUAAAAASUVORK5CYII=" style="width:9px; height:19px" > from <img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAARCAIAAAAzPjmrAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAUNJREFUOE+9VDF2gzAMFT0LydCXEzgnKFk6Ze1mxmbplrEHgLE+QqYuhROUE+QxBN/FlYxNZJ4hLFQLlmX9L9lfJMYYWNOe1gQn7P8k0OU+2ZcaoM4TMrsevLxe2Ctl88P4BmhdIUAUXe8YU0nmoQOy8qFFX5YPDp6hOz6PWckwtoiBKu7TiGBw7rnUETFEQhEC6tEaK8UjIIFfBpl2s/BlzFV9v8EQyNU2paJ0uwN1as+/7+ns4+ryU8nq6yV6qGm7WZmK4iOeyNC6tpGv7hSuxfNmRDXVQf2txPEQVk86HqlV364es84zJc9BwxRCgvRwFNeb1bwzRMoUNKe3fhKmTf9cAC4bOzYZVIZdFYaa3RYr9FPwWOn4muNDkS2nh0CmI+EvE7orLF4XU7ftYBhfLuTHPPEhIdmyeUho2Na01f+mfyAMgWqiKy7ZAAAAAElFTkSuQmCC" style="width:32px; height:17px" > to<img alt="" src="data:image/png;base64,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" style="width:33px; height:17px" > such that <img alt="" src="data:image/png;base64,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" style="width:121px; height:17px" > for all <img alt="" src="data:image/png;base64,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" style="width:83px; height:17px" > and <m:omath><m:r>y</m:r><m:r>∈</m:r><m:r>Ỵ</m:r></m:omath>   برگشت لیپشیتس, جبر حقیقی لیپشیتس, نرم-جمعی در قدرمطلق, نرم یکنواخت. Lipschitz involution‚ norm-additive in modulus‚ real Lipschitz algebra‚ uniform norm. 77 99 http://mmr.khu.ac.ir/browse.php?a_code=A-10-1714-2&slc_lang=fa&sid=1 Mansureh Mohammadi منصوره محمدی s39912131067@phd.araku.ac.ir 10031947532846006745 10031947532846006745 No Arak University دانشگاه اراک Davood Alimohammadi داود علیمحمدی d-alimohammadi@araku.ac.ir 10031947532846006746 10031947532846006746 Yes Arak University دانشگاه اراک