Certain Schur-Hadamard multipliers in the spaces

Author:
Jonathan Arazy

Journal:
Proc. Amer. Math. Soc. **86** (1982), 59-64

MSC:
Primary 47D15; Secondary 46B99, 47B10

DOI:
https://doi.org/10.1090/S0002-9939-1982-0663866-5

MathSciNet review:
663866

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a continuously differentiable function on satisfying for some , and all , and let satisfy for all . Then

**[1]**M. S. Birman and M. Z. Solomjak,*Stieltjes double operator integrals*, Soviet Math. Dokl.**6**(1965), 1567-1571.**[2]**-,*Stieltjes double operator integrals and multiplier problems*, Soviet Math. Dokl.**7**(1966), 1618-1621.**[3]**-,*Remarks on the spectral shift function*, J. Soviet Math.**3**(1975), 408-419.**[4]**M. Š. Birman and M. Z. Solomjak,*Estimates for the singular numbers of integral operators*, Uspehi Mat. Nauk**32**(1977), no. 1(193), 17–84, 271 (Russian). MR**0438186****[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), 1-30.**[6]**Yu. B. Farforovskaya,*Example of a Lipschitz function of self-adjoint operators that gives a nonnuclear increment under a nuclear perturbation*. J. Soviet Math.**4**(1975), 426-433.**[7]**-,*An estimate of the difference**in the classes*, J. Soviet Math.**8**(1977), 146-148.**[8]**-,*An estimate of the norm**for self-adjoint operators*and , J. Soviet Math.**14**(1980), 1133-1149.**[9]**I. C. Gohberg and M. G. Kreĭn,*Introduction to the theory of linear nonselfadjoint operators*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR**0246142****[10]**I. C. Gohberg and M. G. Kreĭn,*Theory and applications of Volterra operators in Hilbert space*, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 24, American Mathematical Society, Providence, R.I., 1970. MR**0264447****[11]**S. Kwapień and A. Pełczyński,*The main triangle projection in matrix spaces and its applications.*, Studia Math.**34**(1970), 43–68. MR**0270118**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0663866-5

Keywords:
spaces,
Schur-Hadamard multipliers,
triangular projection

Article copyright:
© Copyright 1982
American Mathematical Society