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On subsymmetric bases in Fréchet spaces


Author: Wieslaw Sliwa
Journal: Proc. Amer. Math. Soc. 135 (2007), 453-460
MSC (2000): Primary 46A35
DOI: https://doi.org/10.1090/S0002-9939-06-08485-1
Published electronically: August 8, 2006
MathSciNet review: 2255291
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Abstract: It is proved that any non-normable Fréchet space with a semi-symmetric absolute basis is isomorphic to the space $ \omega$ of all scalar sequences. A similar result is shown for quasi-homogeneous absolute bases. It is also proved that any nuclear Fréchet space with a semi-subsymmetric basis is isomorphic to $ \omega$.

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

  • [1] Bessaga C., Pe\lczynski A., On a class of $ B_0$-spaces, Bull. Acad. Pol. Sci., 5(1957), 357-377. MR 0088680 (19:562b)
  • [2] Bessaga C., Pe\lczynski A., W\lasnosci baz w przestrzeniach typu $ B_0$, (in Polish), Prace Matematyczne 3(1959), 123-142. MR 0126691 (23:A3986)
  • [3] Cac N. P., On symmetric Schauder bases in Fréchet spaces, Studia Math. 32(1969), 95-98. MR 0243310 (39:4632)
  • [4] Garling D.J.H., Symmetric bases of locally convex spaces, Studia Math. 30(1968), 163-181. MR 0230105 (37:5670)
  • [5] Rolewicz S., Metric linear spaces, PWN-Polish Scientific Publishers - Warszawa, 1984. MR 0802450 (88i:46004a)
  • [6] Ruckle W., Symmetric coordinate spaces and symmetric bases, Canadian J. Math. 19(1967), 828-839. MR 0236682 (38:4977)
  • [7] Ruckle W., On the characterization of sequence spaces associated with Schauder bases, Studia Math. 28(1967), 279-288. MR 0215049 (35:5894)
  • [8] Singer I., Bases in Banach spaces I, Springer-Verlag Berlin - Heidelberg - New York, 1970. MR 0298399 (45:7451)
  • [9] Terzioglu T., Symmetric bases of nuclear spaces, J. Reine Angew. Math. 252(1972), 200-204. MR 0291758 (45:849)

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Additional Information

Wieslaw Sliwa
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland
Email: sliwa@amu.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-06-08485-1
Keywords: Symmetric, semi-symmetric, semi-subsymmetric, quasi-homogeneous bases
Received by editor(s): October 6, 2004
Received by editor(s) in revised form: September 6, 2005
Published electronically: August 8, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society

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