TY - JOUR

T1 - Operator Ideals on Non-commutative Function Spaces

AU - Oikhberg, Timur

AU - Spinu, Eugeniu

N1 - Funding Information:
The authors acknowledge the generous support of Simons Foundation, via its Travel Grant 210060. They would also like to thank the organizers of Workshop in Linear Analysis at Texas A&M, where part of this work was carried out. Last but not least, they grateful to the reviewer for a careful reading of this paper, and for many useful suggestions.

PY - 2014/8

Y1 - 2014/8

N2 - Suppose X and Y are Banach spaces, and I, J are operator ideals. compact operators). Under what conditions does the inclusion I(X, Y) ⊂ J(X, Y), or the equality I(X, Y) = J(X, Y), hold? We examine this question when I, J are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while X and Y are non-commutative function spaces. Since such spaces are ordered, we also address the same questions for positive parts of such ideals.

AB - Suppose X and Y are Banach spaces, and I, J are operator ideals. compact operators). Under what conditions does the inclusion I(X, Y) ⊂ J(X, Y), or the equality I(X, Y) = J(X, Y), hold? We examine this question when I, J are the ideals of Dunford-Pettis, strictly (co)singular, finitely strictly singular, inessential, or (weakly) compact operators, while X and Y are non-commutative function spaces. Since such spaces are ordered, we also address the same questions for positive parts of such ideals.

KW - Non-commutative function and sequence spaces

KW - operator ideals

UR - http://www.scopus.com/inward/record.url?scp=84904573089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904573089&partnerID=8YFLogxK

U2 - 10.1007/s00020-014-2167-4

DO - 10.1007/s00020-014-2167-4

M3 - Article

AN - SCOPUS:84904573089

SN - 0378-620X

VL - 79

SP - 507

EP - 532

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -