An automatic adjoint theorem and its applications
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- by Junde Wu and Shijie Lu PDF
- Proc. Amer. Math. Soc. 130 (2002), 1735-1741 Request permission
Abstract:
In this paper, we prove the following automatic adjoint theorem: For any sequence spaces $E(X)$ and $F(Y)$, if $E(X)$ has the signed-weak gliding hump property and $A$ is an infinite matrix which transforms $E(X)$ into $F(Y)$, then the transpose matrix $A’$ of $A$ transforms $F(Y)^\beta$ into $E(X)^\beta$, and for any $x\in E(X)$ and $T\in F(Y)^\beta$, $[Ax,T]=[x,A’T]$. That is, the adjoint operator of $A$ automatically exists and is just the transpose matrix $A’$ of $A$. From the theorem we obtain a class of infinite matrix topological algebras $(\lambda ,\mu )$, and prove also a $\lambda$-multiplier convergence theorem of Orlicz-Pettis type. The theorem improves substantially the famous Stiles’ Orlicz-Pettis theorem.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1735-1741
- MSC (2000): Primary 46A45, 47A05
- DOI: https://doi.org/10.1090/S0002-9939-01-06285-2
- MathSciNet review: 1887021