An automatic adjoint theorem and its applications

Authors:
Junde Wu and Shijie Lu

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1735-1741

MSC (2000):
Primary 46A45, 47A05

Published electronically:
December 20, 2001

MathSciNet review:
1887021

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove the following automatic adjoint theorem: For any sequence spaces and , if has the signed-weak gliding hump property and is an infinite matrix which transforms into , then the transpose matrix of transforms into , and for any and , . That is, the adjoint operator of automatically exists and is just the transpose matrix of . From the theorem we obtain a class of infinite matrix topological algebras , and prove also a -multiplier convergence theorem of Orlicz-Pettis type. The theorem improves substantially the famous Stiles' Orlicz-Pettis theorem.

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Additional Information

**Junde Wu**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

Email:
wjd@math.zju.edu.cn

**Shijie Lu**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-01-06285-2

Keywords:
Sequence space,
infinite matrix,
adjoint operator

Received by editor(s):
June 27, 2000

Received by editor(s) in revised form:
December 7, 2000

Published electronically:
December 20, 2001

Additional Notes:
This research was partially supported by the National Natural Science Foundation of China

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2001
American Mathematical Society