PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Isometries of perfect norm ideals of compact operators

Volume 241 / 2018

Behzod Aminov, Vladimir Chilin Studia Mathematica 241 (2018), 87-99 MSC: Primary 46L52; Secondary 46L51, 46B04. DOI: 10.4064/sm170306-19-4 Published online: 28 September 2017

Abstract

It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\mathcal C_E \not =\mathcal C_{2}$ of compact operators, acting in a complex separable infinite-dimensional Hilbert space $\mathcal H$, there exist unitary operators $u$ and $v$ on $\mathcal H$ such that $V(x) = uxv$ for all $x\in \mathcal C_E$ or $V(x) = ux^tv$ for all $x \in \mathcal C_E$, where $x^t $ is the transpose of $x$ with respect to a fixed orthonormal basis for $\mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $\mathcal C_E \not =\mathcal C_{2}$ is a linear isometry on $\mathcal C_E$.

Authors

  • Behzod AminovNational University of Uzbekistan
    Tashkent, 700174, Uzbekistan
    e-mail
    e-mail
  • Vladimir ChilinNational University of Uzbekistan
    Tashkent, 700174, Uzbekistan
    e-mail
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image