
Accession Number : AD0727277
Title : Bounded Generators of Linear Spaces,
Corporate Author : CARNEGIEMELLON 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 seminorms 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