Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On $ FK$-spaces which are boundedness domains

Author: Glenn Meyers
Journal: Proc. Amer. Math. Soc. 46 (1974), 38-42
MSC: Primary 46A45; Secondary 40J05
MathSciNet review: 0372584
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An open question in summability theory is to characterize those FK-spaces, $ E$, which are boundedness domains (i.e., $ E = {m_A}$ for some infinite matrix $ A$). As a partial solution to this problem we give necessary and sufficient conditions for an FK space $ E$, which has the $ T$-sectional boundedness property, to be equal to $ {m_A}$ for some row-finite $ A$.

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

  • [1] G. Bennett, Ph.D. thesis, Cambridge University.
  • [2] -, A new class of sequence spaces with applications in summability theory, J. Reine Angew. Math. (to appear). MR 0344846 (49:9585)
  • [3] M. Buntinas, On Toeplitz sections in sequence spaces (to appear). MR 0410163 (53:13913)
  • [4] G. Meyers, On Toeplitz sections in FK-spaces, Studia Math. 51 (to appear). MR 0348445 (50:943)
  • [5] A. Wilansky, Functional analysis, Blaisdell, New York, 1964. MR 30 #425. MR 0170186 (30:425)
  • [6] A. Wilansky and K. Zeller, A biorthogonal system which is not a Toeplitz basis, Bull. Amer. Math. Soc. 69 (1963), 725-726. MR 27 #1802. MR 0151819 (27:1802)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A45, 40J05

Retrieve articles in all journals with MSC: 46A45, 40J05

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society