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

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

Published electronically:
June 2, 2004

MathSciNet review:
2085164

Full-text PDF

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]**J. Ball, Interpolation problems and Toeplitz operators on multiply connected domains, Integral Eqs. and Operator Theory, 4 (1981), 172-184.MR**82i:47036****[BG]**J. Ball and I. Gohberg, A commutant lifting theorem for triangular matrices with diverse applications, Integral Eqs. and Operator Theory, 8 (1985), 205-267. MR**86i:47006****[BMSW]**B. Barnes, G. Murphy, R. Smyth, and T. T. West, Riesz and Fredholm Theory in Banach Algebras, Research Notes in Math. 67, Pitman, Boston, 1982.MR**84a:46108****[CPY]**S. Caradus, W. Pfaffenberger, and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Lecture Notes in Pure and Applied Math., Vol. 9, Marcel Dekker, New York, 1974. MR**54:3434****[D]**R. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. MR**34:3315****[DS]**N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York, 1964. MR**90g:47001a****[E]**M. Embry, Factorization of operators on a Banach space, Proc. Amer. Math. Soc. 38 (1973), 587-590. MR**47:849****[F]**L. Fialkow, Structural properties of elementary operators, Elementary Operators & Applications, M. Mathieu, Editor, World Scientific, Singapore, 1992. MR**93i:47042****[G]**S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.MR**34:580****[H]**R. Harte, Invertibility and Singularity for Bounded Linear Operators, Pure and Applied Math., Marcel Dekker, New York and Basel, 1988. MR**89d:47001****[KMT]**E. Katsoulis, R. Moore, and T. Trent, Interpolation in nest algebras and applications to operator corona theorems, J. Operator Theory 29 (1983), 115-123. MR**95b:47052****[LT]**D. Lay and A. Taylor, Introduction to Functional Analysis, John Wiley and Sons, New York, 1980. MR**81b:46001****[RR]**M. Rosenblum and J. Rovnyak, Hardy Classes and Operator Theory, Dover, Mineola, New York, 1997. MR**97j:47002**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
47A05

Retrieve articles in all journals with MSC (2000): 47A05

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