We study three closely related concepts in the context of the Banach algebra C₀(X,A). We show that, to a certain extent, Segal extensions, norm irregularity and the existence of approximate identities in C₀(X,A) can be deduced from the corresponding features of A and vice versa. Extensive use is made of the multiplier norm and the tensor product representation of C₀(X,A).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-2-1,
author = {Jussi Mattas},
title = {Segal algebras, approximate identities and norm irregularity in C0(X,A)},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {99-112},
zbl = {1285.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-2-1}
}
Jussi Mattas. Segal algebras, approximate identities and norm irregularity in C₀(X,A). Studia Mathematica, Tome 215 (2013) pp. 99-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm215-2-1/