Majorization, range inclusion, and factorization for bounded linear operators

Barnes, Bruce

doi:10.1090/S0002-9939-04-07495-7

Majorization, range inclusion, and factorization for bounded linear operators
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Proc. Amer. Math. Soc. 133 (2005), 155-162 Request permission

Abstract:

In this paper, relationships among the concepts, majorization, range inclusion, and factorization, are studied in a general setting for bounded linear operators. Some applications of these concepts are given.

References

Joseph A. Ball, Interpolation problems and Toeplitz operators on multiply connected domains, Integral Equations Operator Theory 4 (1981), no. 2, 172–184. MR 606130, DOI 10.1007/BF01702379
Joseph A. Ball and Israel Gohberg, A commutant lifting theorem for triangular matrices with diverse applications, Integral Equations Operator Theory 8 (1985), no. 2, 205–267. MR 782618, DOI 10.1007/BF01202814
Bruce A. Barnes, G. J. Murphy, M. R. F. Smyth, and T. T. West, Riesz and Fredholm theory in Banach algebras, Research Notes in Mathematics, vol. 67, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 668516
S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR 0415345
R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 203464, DOI 10.1090/S0002-9939-1966-0203464-1
Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
Mary R. Embry, Factorization of operators on Banach space, Proc. Amer. Math. Soc. 38 (1973), 587–590. MR 312287, DOI 10.1090/S0002-9939-1973-0312287-8
Lawrence A. Fialkow, Structural properties of elementary operators, Elementary operators and applications (Blaubeuren, 1991) World Sci. Publ., River Edge, NJ, 1992, pp. 55–113. MR 1183937
Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
E. G. Katsoulis, R. L. Moore, and T. T. Trent, Interpolation in nest algebras and applications to operator corona theorems, J. Operator Theory 29 (1993), no. 1, 115–123. MR 1277968
Angus Ellis Taylor and David C. Lay, Introduction to functional analysis, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR 564653
Marvin Rosenblum and James Rovnyak, Hardy classes and operator theory, Dover Publications, Inc., Mineola, NY, 1997. Corrected reprint of the 1985 original. MR 1435287