TY - GEN

T1 - Approximation of p-summing operators by adjoints

AU - Reinov, Oleg I.

PY - 2012

Y1 - 2012

N2 - We consider the following question for the ideals Π p of absolutely p-summing operators: Is it true that, for given Banach spaces X and Y, the unit ball of the space Π p(X,Y) is dense, for some natural topology, in the unit ball of the space Π p(X,Y**) or in the unit ball of the corresponding space Π p dual(Y*,X*):=(U:Y*→X*ιU* ι XεΠ p(X,Y**)? As "natural topologies", we consider strong and weak operator topologies, compact-open topology, topology of X × Y*-convergence etc.

AB - We consider the following question for the ideals Π p of absolutely p-summing operators: Is it true that, for given Banach spaces X and Y, the unit ball of the space Π p(X,Y) is dense, for some natural topology, in the unit ball of the space Π p(X,Y**) or in the unit ball of the corresponding space Π p dual(Y*,X*):=(U:Y*→X*ιU* ι XεΠ p(X,Y**)? As "natural topologies", we consider strong and weak operator topologies, compact-open topology, topology of X × Y*-convergence etc.

KW - Absolutely p-summing operators

KW - Banach tensor product

KW - Pointwise convergence

UR - http://www.scopus.com/inward/record.url?scp=84861943701&partnerID=8YFLogxK

U2 - 10.1063/1.4724114

DO - 10.1063/1.4724114

M3 - Conference contribution

SN - 9780735410497

T3 - AIP Conference Proceedings

SP - 32

EP - 36

BT - 5th International Conference on Research and Education in Mathematics, ICREM5

PB - American Institute of Physics

T2 - 5th International Conference on Research and Education in Mathematics, ICREM5

Y2 - 22 October 2011 through 24 October 2011

ER -