Unusual Traces on Operator Ideals

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

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Extension of Finite Rank Operators and Operator Ideals with the Property (I)

Mathematische Nachrichten ◽

10.1002/1522-2616(200205)238:1<144::aid-mana144>3.0.co;2-y ◽

2002 ◽

Vol 238 (1) ◽

pp. 144-159

Author(s):

Frank Oertel

Keyword(s):

Finite Rank ◽

Operator Ideals ◽

Finite Rank Operators

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Cartan subalgebras of operator ideals

Indiana University Mathematics Journal ◽

10.1512/iumj.2016.65.5784 ◽

2016 ◽

Vol 65 (1) ◽

pp. 1-37 ◽

Cited By ~ 1

Author(s):

Daniel Beltita ◽

SASMITA PATNAIK ◽

Gary Weiss

Keyword(s):

Operator Ideals ◽

Cartan Subalgebras

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CLASSES OF SEQUENTIALLY LIMITED OPERATORS

Glasgow Mathematical Journal ◽

10.1017/s0017089515000348 ◽

2015 ◽

Vol 58 (3) ◽

pp. 573-586

Author(s):

JAN H. FOURIE ◽

ELROY D. ZEEKOEI

Keyword(s):

Banach Space ◽

Vector Space ◽

Normed Space ◽

Operator Ideal ◽

Operator Ideals ◽

Ideal Norm ◽

Relevant Operator

AbstractThe purpose of this paper is to present a brief discussion of both the normed space of operator p-summable sequences in a Banach space and the normed space of sequentially p-limited operators. The focus is on proving that the vector space of all operator p-summable sequences in a Banach space is a Banach space itself and that the class of sequentially p-limited operators is a Banach operator ideal with respect to a suitable ideal norm- and to discuss some other properties and multiplication results of related classes of operators. These results are shown to fit into a general discussion of operator [Y,p]-summable sequences and relevant operator ideals.

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