Multirectangular invariants for power Köthe spaces

• Published in: Journal of mathematical analysis and applications Vol. 297; no. 2; pp. 673 - 695
• Main Authors: Chalov, P., Terzioğlu, T., Zahariuta, V.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15-09-2004
• Subjects: Compound invariants; First type power Köthe spaces; Linear topological invariants; m-rectangular characteristics; Quasidiagonal isomorphism; Compound invariants; m-rectangular characteristics; Quasidiagonal isomorphism; Linear topological invariants; First type power Köthe spaces
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2004.04.034

Using some new linear topological invariants, isomorphisms and quasidiagonal isomorphisms are investigated on the class of
first type power Köthe spaces [Proceedings of 7th Winter School in Drogobych, 1976, pp. 101–126; Turkish J. Math. 20 (1996) 237–289; Linear Topol. Spaces Complex Anal. 2 (1995) 35–44]. This is the smallest class of Köthe spaces containing all Cartesian and projective tensor products of power series spaces and closed with respect to taking of basic subspaces (closed linear hulls of subsets of the canonical basis). As an application, it is shown that isomorphic spaces from this class have, up to quasidiagonal isomorphisms, the same basic subspaces of finite (infinite) type.