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)



Remark on Walter's inequality for Schur multipliers

Author: Marek Bożejko
Journal: Proc. Amer. Math. Soc. 107 (1989), 133-136
MSC: Primary 47B38; Secondary 42B15
MathSciNet review: 1007285
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We extend and give another proof of Walter's inequality: For a linear operator $ T \in L({l^2}(X))$

$\displaystyle \vert\vert T\vert\vert _{{V_2}(X)}^2 \leq \vert\vert\,\vert T{\ve... ...}\vert{\vert _{{V_2}(X)}}\vert\vert\,\vert T{\vert _r}\vert{\vert _{{V_2}(X)}},$

where $ {V_2}(X)$ is the Banach algebra of Schur multipliers on $ L({l^2}(X))$ and $ \vert T{\vert _l} = {(TT)^{*1/2}},\vert T{\vert _r} = \vert{T^*}{\vert _l}$.

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

  • [Be] G. Bennett, Schur multipliers,Duke Math. J. 44 (1977), 603-639. MR 0493490 (58:12490)
  • [Bo] M. Bozejko, Positive definite bounded matrices and a characterization of amenable groups, Proc. Amer. Math. Soc. 95 (1985), 357-360. MR 806070 (87h:43006)
  • [GK] I. C. Goh'berg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Amer. Math. Soc., Providence, R. I., 1969. MR 0246142 (39:7447)
  • [H] C. Herz, Une generalization de le notion de transformé le Fourier-Stieltjes, Ann. Inst. Fourier (Grenoble), 24 (1974), 145-157. MR 0425511 (54:13466)
  • [W] M. E. Walter, On the Norm of a Schur product, Linear Algebra Appl. 79 (1986), 209-213. MR 847198 (87j:15048)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38, 42B15

Retrieve articles in all journals with MSC: 47B38, 42B15

Additional Information

Keywords: Schur multipliers, Schur product
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society