Positive operators on a Banach space and the Fejér-Riesz theorem
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- by A. G. Miamee and H. Salehi
- Proc. Amer. Math. Soc. 56 (1976), 189-192
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399950-0
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Abstract:
The Fejér and Riesz theorem on the factorization of nonnegative trigonometric polynomials is extended to the nonnegative operator valued trigonometric polynomials on a Banach space. The work is based on the analysis of quasi square roots of nonnegative operator valued functions on a Banach space.References
- Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
- A. G. Miamee and H. Salehi, Factorization of positive operator valued functions on a Banach space, Indiana Univ. Math. J. 24 (1974/75), 103–113. MR 350478, DOI 10.1512/iumj.1974.24.24008
- Murray Rosenblatt, A multi-dimensional prediction problem, Ark. Mat. 3 (1958), 407–424. MR 92332, DOI 10.1007/BF02589495
- Marvin Rosenblum, Vectorial Toeplitz operators and the Fejér-Riesz theorem, J. Math. Anal. Appl. 23 (1968), 139–147. MR 227794, DOI 10.1016/0022-247X(68)90122-4
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 189-192
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399950-0
- MathSciNet review: 0399950