Linear equations in subspaces of operators
Authors:
R. L. Moore and T. T. Trent
Journal:
Proc. Amer. Math. Soc. 128 (2000), 781788
MSC (1991):
Primary 47D25
Published electronically:
March 3, 1999
MathSciNet review:
1626454
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Abstract: Given a subspace of operators on a Hilbert space, and given two operators and (not necessarily in ), when can we be certain that there is an operator in such that ? If there is one, can we find some bound for its norm? These questions are the subject of a number of papers, some by the present authors, and mostly restricted to the case where is a reflexive algebra. In this paper, we relate the broader question involving operator subspaces to the question about reflexive algebras, and we examine a new method of forming counterexamples, which simplifies certain constructions and answers an unresolved question. In particular, there is a simple set of conditions that are necessary for the existence of a solution in the reflexive algebra case; we show that  even in the case where the corank of is onethese conditions are not in general sufficient.
 1.
R.
G. Douglas, On majorization, factorization, and
range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413–415. MR 0203464
(34 #3315), http://dx.doi.org/10.1090/S00029939196602034641
 2.
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
(95b:47052)
 3.
R. Moore and T. Trent, Solving Operator Equations in Nest Algebras, Houston Journal of Mathematics, to appear.
 4.
R. Moore, and T. Trent, Interpolation in Inflated Hilbert Spaces, Proc. Amer. Math. Soc. Journal of Operator Theory, to appear. CMP 98:01
 1.
 R. G. Douglas, On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space, Proc. Amer. Math. Soc. 17 (1966), 413415.MR 34:3315
 2.
 E. Katsoulis, R. Moore, and T. Trent, Interpolation in Nest Algebras and Applications to Operator Corona Theorems, Journal of Operator Theory 29 (1993), 115123. MR 95b:47052
 3.
 R. Moore and T. Trent, Solving Operator Equations in Nest Algebras, Houston Journal of Mathematics, to appear.
 4.
 R. Moore, and T. Trent, Interpolation in Inflated Hilbert Spaces, Proc. Amer. Math. Soc. Journal of Operator Theory, to appear. CMP 98:01
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Additional Information
R. L. Moore
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 354870350
T. T. Trent
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 354870350
DOI:
http://dx.doi.org/10.1090/S0002993999050649
PII:
S 00029939(99)050649
Received by editor(s):
April 22, 1998
Published electronically:
March 3, 1999
Communicated by:
David R. Larson
Article copyright:
© Copyright 1999 American Mathematical Society
