Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Perfect matrix methods


Authors: D. J. Fleming and P. G. Jessup
Journal: Proc. Amer. Math. Soc. 29 (1971), 319-324
MSC: Primary 40.31
MathSciNet review: 0279484
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {e_i} = ({\delta _{ij}})_{j = 1}^\infty ,\Delta = ({e_i})_{i = 1}^\infty $ and let A be an infinite matrix which maps E into E where E is an FK-space with Schauder basis $ \Delta $. Necessary and sufficient conditions in terms of the matrix A are obtained for E to be dense in the summability space $ {E_A} = \{ x \vert {Ax \in E\} }$ and conditions are obtained to guarantee that $ {E_A}$ has Schauder basis $ \Delta $. Finally it is shown that if weak and strong sequential convergence coincide in E then in $ {E_A}$ the series $ \sum {_k{x_k}{e_k}} $ converges to x strongly if and only if it converges to x weakly.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 40.31

Retrieve articles in all journals with MSC: 40.31


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279484-X
PII: S 0002-9939(1971)0279484-X
Keywords: Perfect matrix method, associative matrix method, property P, type M, type $ {M^ \ast }$
Article copyright: © Copyright 1971 American Mathematical Society