Open AccessM(r,s)-inequality for K(X,Y) in L(X,Y)
Author(s) -
Rainis Haller,
Marje Johanson,
Eve Oja
Publication year - 2007
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2007.11.07
Subject(s) - ideal (ethics) , banach space , mathematics , subspace topology , combinatorics , span (engineering) , discrete mathematics , mathematical analysis , philosophy , civil engineering , epistemology , engineering
We study Banach spaces X and Y for which the subspace of all compact operators K(X,Y) forms an ideal satisfying the M(r,s)-inequality in the space of all continuous linear operators L(X,Y). We prove that K(X,Y) is an M(r12r2,s12s2)- and an M(r1r22,s1s22)-ideal in L(X,Y) whenever K(X) and L(Y) are M(r1,s1)- and M(r2,s2)-ideals in span(K(X)∪IX) and span(K(Y)∪IY), respectively, with r1+s1/2>1 and r2+s2/2>1. Our results extend some well-known results on M-ideals.