Accession Number : AD0727277

Title :   Bounded Generators of Linear Spaces,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA

Personal Author(s) : Seidman,T. ; Ito,T.

Report Date : 1971

Pagination or Media Count : 9

Abstract : Let S sub phi = (x epsilon X: (sup sub alpha) (phi sub alpha) (x) < infinity where phi = (phi sub alpha) is a family of semi-norms determining the topology of X. It is shown that phi may be chosen so S sub phi is dense if X has a bounded generating set if there is a continuous norm on X star. It is shown that these conditions hold for separable Frechet spaces and for quotients of products of Banach spaces. An example is given of a Frechet space containing no bounded generating set thus contradicting an assertion of L. Mate that S sub phi is dense for Frechet spaces. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, BANACH SPACE), HILBERT SPACE, SET THEORY, SEQUENCES, TOPOLOGY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE