Certain SchurHadamard multipliers in the spaces
Author:
Jonathan Arazy
Journal:
Proc. Amer. Math. Soc. 86 (1982), 5964
MSC:
Primary 47D15; Secondary 46B99, 47B10
MathSciNet review:
663866
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Abstract 
References 
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Additional Information
Abstract: Let be a continuously differentiable function on satisfying for some , and all , and let satisfy for all . Then is a SchurHadamard multiplier from into for all , satisfying and .
 [1]
M. S. Birman and M. Z. Solomjak, Stieltjes double operator integrals, Soviet Math. Dokl. 6 (1965), 15671571.
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, Stieltjes double operator integrals and multiplier problems, Soviet Math. Dokl. 7 (1966), 16181621.
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Š. Birman and M.
Z. Solomjak, Estimates for the singular numbers of integral
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Ju. L. Daleckii and S. G. Krein, Integration and differentation of functions of hermitian operators and applications to the theory of perturbations, Amer. Math. Soc. Transl. (2) 47 (1965), 130.
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Yu. B. Farforovskaya, Example of a Lipschitz function of selfadjoint operators that gives a nonnuclear increment under a nuclear perturbation. J. Soviet Math. 4 (1975), 426433.
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, An estimate of the difference in the classes , J. Soviet Math. 8 (1977), 146148.
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, An estimate of the norm for selfadjoint operators and , J. Soviet Math. 14 (1980), 11331149.
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C. Gohberg and M.
G. Kreĭn, Introduction to the theory of linear
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I.
C. Gohberg and M.
G. Kreĭn, Theory and applications of Volterra operators in
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0270118 (42 #5011)
 [1]
 M. S. Birman and M. Z. Solomjak, Stieltjes double operator integrals, Soviet Math. Dokl. 6 (1965), 15671571.
 [2]
 , Stieltjes double operator integrals and multiplier problems, Soviet Math. Dokl. 7 (1966), 16181621.
 [3]
 , Remarks on the spectral shift function, J. Soviet Math. 3 (1975), 408419.
 [4]
 , Estimates of singular numbers of integral operators, Russian Math. Surveys, 32 (1977), 1589. MR 0438186 (55:11104)
 [5]
 Ju. L. Daleckii and S. G. Krein, Integration and differentation of functions of hermitian operators and applications to the theory of perturbations, Amer. Math. Soc. Transl. (2) 47 (1965), 130.
 [6]
 Yu. B. Farforovskaya, Example of a Lipschitz function of selfadjoint operators that gives a nonnuclear increment under a nuclear perturbation. J. Soviet Math. 4 (1975), 426433.
 [7]
 , An estimate of the difference in the classes , J. Soviet Math. 8 (1977), 146148.
 [8]
 , An estimate of the norm for selfadjoint operators and , J. Soviet Math. 14 (1980), 11331149.
 [9]
 I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Transl. Math. Monos., Vol. 18, Amer. Math. Soc., Providence, R. I., 1969. MR 0246142 (39:7447)
 [10]
 , Theory and applications of Volterra operators in Hilbert spaces, Transl. Math. Monos., Vol. 24, Amer. Math. Soc, Providence, R. I., 1970. MR 0264447 (41:9041)
 [11]
 S. Kwapien and A. Pelczynski, The main triangular projection in matrix spaces and its applications, Studia Math. 34 (1970), 4368. MR 0270118 (42:5011)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206638665
PII:
S 00029939(1982)06638665
Keywords:
spaces,
SchurHadamard multipliers,
triangular projection
Article copyright:
© Copyright 1982 American Mathematical Society
