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Strong Birkhoff–James Orthogonality of Compact Operators on Hilbert Spaces

pregledni rad (znanstveni)

pregledni rad (znanstveni)

Strong Birkhoff–James Orthogonality of Compact Operators on Hilbert Spaces

Vrsta prilog sa skupa (u zborniku)
Tip pregledni rad (znanstveni)
Godina 2024
Nadređena publikacija Women in Analysis and PDE
Stranice str. 17-26
DOI 10.1007/978-3-031-57005-6_3
ISSN 2297-0215
EISSN 2297-024X
Status objavljeno

Sažetak

Let $H$ be an infinite-dimensional Hilbert space, $AinBbb K(H)$, $Ane 0$ and $Bin B(H).$ We prove that $A$ and $B$ satisfy
the inequality $|A+CBD|ge |A|$ for all $C,Din B(H)$ if and only if the rank of the operator $B^*$ is strictly less than the dimension of the kernel of the operator $A^*A-|A|^2I.$

Ključne riječi

(strong) Birkhoff--James orthogonality, compact operator