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Functional analysis and its applications
September 17, 2020 09:00–10:00
 


Isometries of Banach ideals of compact operators

B. R. Aminov, V. I. Chilin

National University of Uzbekistan named after M. Ulugbek, Tashkent

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Abstract: Let $H$ be a complex separable infinite-dimensional Hilbert space and let $J \ne C_2$ be a perfect Banach symmetric ideal of compact linear operators acting in $H$. We show that for any surjective linear isometry $V$ on $J$ there are unitary operators $u$ and $v$ on $H$ such that $V(x) = uxv$ or $V(x) = ux^tv$ for all $x$ in $J$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $H$.

Website: https://us02web.zoom.us/j/88171497327

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