Results 251 to 260 of about 2,185,505 (314)

Operator Ideals Generalizing the Ideal of Strictly Singular Operators

Mathematische Nachrichten, 1980
AbstractIt is well‐known that an operator T ∈ L(E, F) is strictly singular if ∥Tx∥≧λ∥x∥ on a subspace Z ⊂ E implies dim Z < + ∞. The present paper deals with ideals of operators defined by a condition — ∥Tx∥≧λ∥x∥ on an infinite‐dimensional subspace Z ⊂ E implies Z ∉ F — F being a „quasi‐injective”︁ class of BANACH spaces.
openaire   +1 more source

E-Operator Ideals Determined by Banach Spaces with Unconditional Bases

Mediterranean Journal of Mathematics, 2022
Ju Myung Kim, Pablo Turco, Bentuo Zheng
semanticscholar   +1 more source

Unusual Traces on Operator Ideals

Mathematische Nachrichten, 1987
Let H be a separable Hilbert space and B(H) (resp. \(B_ 0(H))\) the space of all bounded linear operators (resp. compact operators) defined on H. Given an ideal J in \(B_ 0(H)\) a trace on J is a linear functional \(\tau\) on J so that (1) \(\tau (P)=1\) if P is a rank one projection, (2) \(\tau (XY)=\tau (YX)\) if \(X\in J\) and \(Y\in B(H).\) We say ...
openaire   +2 more sources

Operator ideals generated by strongly Lorentz sequence spaces

Advances in Operator Theory, 2021
D. Achour, A. Attallah
semanticscholar   +1 more source

On some geometric properties of generalized Musielak-Orlicz sequence space and corresponding operator ideals

, 2014
Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold {\Phi}}^{A}(X)$ is introduced.
Amit Maji, P. D. Srivastava
semanticscholar   +1 more source

Invariant Ideals of Positive Operators

SIAM Review, 1974
This paper gives a systematic treatment of generalizations of the Perron–Frobenius theorems for nonnegative matrices to semigroups of positive operators acting on ordered Banach spaces with order units.
openaire   +1 more source

Operator Ideals on Non-commutative Function Spaces

, 2013
Suppose X and Y are Banach spaces, and $${{\mathcal{I}}}$$I , $${{\mathcal{J}}}$$J are operator ideals. compact operators). Under what conditions does the inclusion $${\mathcal{I}(X,Y) \subset \mathcal{J}(X,Y)}$$I(X,Y)⊂J(X,Y) , or the equality ...
T. Oikhberg, E. Spinu
semanticscholar   +1 more source

Ideals in algebras of unbounded operators. II

Mathematische Nachrichten, 1979
AbstractA general procedure is given to get ideals in algebras of unbounded operators starting with ideals in ℬ︁(ℋ︁). Algebraical and topological properties of ideals obtained in this manner from the well‐known symmetrically‐normed ideals Sϕ(ℋ︁) are described.
openaire   +4 more sources

The Lipschitz injective hull of Lipschitz operator ideals and applications

Banach Journal of Mathematical Analysis, 2020
D. Achour, E. Dahia, Pablo Turco
semanticscholar   +1 more source

The Existence of Singular Traces on Simply Generated Operator Ideals

, 2020
A. Pietsch
semanticscholar   +1 more source