On Tensor Products of Quasi-Banach Spaces

Autor:	Hansen, Markus
Jazyk:	angličtina
Rok vydání:	2010
Předmět:	tensor product of distributions p-norm p-nuclear tensor norm FOS: Mathematics quasi-norm ddc:510 algebraic tensor product injective tensor norm Mathematics
Zdroj:	SAM Research Report, 2010-31
Popis:	Due to applications in approximation theory we are interested in tensor products of quasi-Banach spaces. Though a general abstract theory seems not possible beyond basic topological issues because the dual spaces are possibly trivial, we aim at extending some basic notions like crossnorms, reasonable and uniform norms. In the present paper this is done for quasi- Banach spaces with separating duals, and this condition turns out to be the (in a certain sense) minimal requirement. Moreover, we study extensions of the classical injective and p-nuclear tensor norms to quasi Banach spaces. In particular, we give a sufficient condition for the $p$nuclear quasi-norms to be crossnorms, which particularly applies to the case of weighted $l_p$-sequence spaces. SAM Research Report, 2010-31
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::02f7d4ee5297d589e5f4fea440e68f39 https://hdl.handle.net/20.500.11850/154930 Zobrazit plný text záznamu