Majorization, range inclusion, and factorization for bounded linear operators

Author:
Bruce A. Barnes

Journal:
Proc. Amer. Math. Soc. **133** (2005), 155-162

MSC (2000):
Primary 47A05

Published electronically:
June 2, 2004

MathSciNet review:
2085164

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[B]**Joseph A. Ball,*Interpolation problems and Toeplitz operators on multiply connected domains*, Integral Equations Operator Theory**4**(1981), no. 2, 172–184. MR**606130**, 10.1007/BF01702379**[BG]**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**, 10.1007/BF01202814**[BMSW]**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****[CPY]**S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood,*Calkin algebras and algebras of operators on Banach spaces*, Marcel Dekker, Inc., New York, 1974. Lecture Notes in Pure and Applied Mathematics, Vol. 9. MR**0415345****[D]**R. G. Douglas,*On majorization, factorization, and range inclusion of operators on Hilbert space*, Proc. Amer. Math. Soc.**17**(1966), 413–415. MR**0203464**, 10.1090/S0002-9939-1966-0203464-1**[DS]**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****[E]**Mary R. Embry,*Factorization of operators on Banach space*, Proc. Amer. Math. Soc.**38**(1973), 587–590. MR**0312287**, 10.1090/S0002-9939-1973-0312287-8**[F]**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****[G]**Seymour Goldberg,*Unbounded linear operators: Theory and applications*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR**0200692****[H]**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****[KMT]**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****[LT]**Angus Ellis Taylor and David C. Lay,*Introduction to functional analysis*, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR**564653****[RR]**Marvin Rosenblum and James Rovnyak,*Hardy classes and operator theory*, Dover Publications, Inc., Mineola, NY, 1997. Corrected reprint of the 1985 original. MR**1435287**

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Additional Information

**Bruce A. Barnes**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email:
barnes@darkwing.uoregon.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07495-7

Keywords:
Bounded linear operator,
majorization,
range inclusion,
factorization

Received by editor(s):
August 1, 2003

Received by editor(s) in revised form:
September 9, 2003

Published electronically:
June 2, 2004

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society