TY - GEN

T1 - lSome Remarks on Approximation Properties with Applications

AU - Reinov, Oleg

PY - 2016

Y1 - 2016

N2 - We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the properties like the AP(s) or AP((s,w)) for s is an element of(0, 1], which give us the possibility to identify the spaces of s-nuclear and (s, w)-nuclear operators with the corresponding tensor products (e.g., related to Lorentz sequence spaces). Some applications are given (in particular, we present not difficult proofs of the trace-formulas of GrothendieckLidskii type for several ideals of nuclear operators).

AB - We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the properties like the AP(s) or AP((s,w)) for s is an element of(0, 1], which give us the possibility to identify the spaces of s-nuclear and (s, w)-nuclear operators with the corresponding tensor products (e.g., related to Lorentz sequence spaces). Some applications are given (in particular, we present not difficult proofs of the trace-formulas of GrothendieckLidskii type for several ideals of nuclear operators).

KW - Nuclear operator

KW - tensor product

KW - approximation property

KW - eigen-value

KW - SUBSPACES

KW - OPERATORS

M3 - статья в сборнике материалов конференции

SN - 978-3-319-27840-7

T3 - Trends in Mathematics

SP - 371

EP - 394

BT - ORDERED STRUCTURES AND APPLICATIONS

A2 - DeJeu, M

A2 - DePagter, B

A2 - VanGaans, O

A2 - Veraar, M

PB - Birkhäuser Verlag AG

Y2 - 22 July 2013 through 26 July 2013

ER -