Titlebook: Recent Advances in Operator Theory and Applications; Tsuyoshi Ando,Raúl E. Curto,Woo Young Lee Conference proceedings 2009 Birkhäuser Base

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A New Majorization Induced by Matrix Order,Let . be a non-decreasing function on . and . an increasing function on .. Then . is said to be . by ., in symbols . if . ⊂ . and . ○ .. is operator monotone on .(.), that is if .(.), .(.) ⊂ ., .(.) ≦ .(.) ⇒ .(.) ≦ .(.). We will give a condition for . in order that ..

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,, Functional Calculus and Characterization of Domains of Fractional Powers,Characterization of the domains of fractional powers of linear operators is very important in the study of (linear or nonlinear) abstract parabolic evolution equations. In this paper we present a new method of utilizing the . . functional calculus of linear operators.

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Tsuyoshi Ando,Raúl E. Curto,Woo Young LeeIncludes supplementary material:

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Relaxed Commutant Lifting: An Equivalent Version and a New Application,axed commutant lifting problem. Using this connection a description of all solutions of the former problem is given. Also a new application, involving bounded operators induced by .. operator-valued functions, is presented.

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Variants of Ando-Hiai Inequality,se of Kubo-Ando. In this context, the Furuta inequality is understood as the one-sided version (the case of . = 1): If . . . ≤ ., then . As a consequence, the Furuta inequality has an alternative simple proof. In addition, we point out that the obtained inequality is understood as the case . = 1 in the grand Furuta inequality.

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,Spectral Consequences due to General Hölder’s Inequalities and Domination of Semigroups,plies a kernel estimate . with 1 / . + 1 / . = 1, . positive constants. The kernel estimate allows to study the spectra of . + .. if the spectrum of . is known. For instance we give conditions such that the essential and absolutely continuous spectra are stable. Moreover, one can prove the limiting