Some reverse inequalities for matrices on indefinite inner product spaces

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• 作者：Ali Taghavi ^{taghavi@umz.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Haji Mohammad Nazari ^{m.nazari@stu.umz.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Vahid Darvish ; ^{vahid.darvish@mail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Reverse Schwarz inequality ; Reverse Heinz&ndash ; Kato&ndash ; Furuta inequality ; Indefinite inner product ; Minkowski inner product
• 刊名：Indagationes Mathematicae
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：27
• 期：1
• 页码：11-19
• 全文大小：179 K

文摘

In this paper, we generalize the following inequality due to N. Bebiano et al which states that for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si103.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=e131f33ddbf96617c573628006f08aeb" title="Click to view the MathML source">Jclass="mathContainer hidden">class="mathCode">$J$-contraction class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si168.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=8d9c136307169669ab173a4d1fbafa0a" title="Click to view the MathML source">T∈M_nclass="mathContainer hidden">class="mathCode">$T\in {\mathcal{M}}_n$ for any class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si174.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=67d77764edc58053bdd99b27584d4547" title="Click to view the MathML source">x,y∈Cⁿclass="mathContainer hidden">class="mathCode">$x,y\in C^n$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si157.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=866e7b24a8ba31bba7935c9902ca9fca" title="Click to view the MathML source">xclass="mathContainer hidden">class="mathCode">$x$ or class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si158.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=59b076d9f41e1c64c9320a83857eabb0" title="Click to view the MathML source">yclass="mathContainer hidden">class="mathCode">$y$ time-like and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0019357715000476&_mathId=si7.gif&_user=111111111&_pii=S0019357715000476&_rdoc=1&_issn=00193577&md5=1eb0bb99981294bfbcb542b9919809df" title="Click to view the MathML source">α∈[0,1]class="mathContainer hidden">class="mathCode">$\alpha \in [0,1]$. The above inequality gives a reverse weighted mixed Schwarz inequality. Also, we prove some reverse inequalities for indefinite inner product space. Moreover, we establish some refinements for the reverse of Schwarz inequality as well.