Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Substrictly cyclic operators

Author(s): Ben Mathes
Journal: Proc. Amer. Math. Soc. 137 (2009), 3757-3762.
MSC (2000): Primary 46B28, 47L50, 46L07; Secondary 46H10
Posted: May 28, 2009
MathSciNet review: 2529884
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We initiate the study of substrictly cyclic operators and algebras. As an application of this theory, we are able to give a description of the strongly closed ideals in the commutant of the Volterra operator, and quite a bit more.

References:

1.: R. Bolstein, W. Wogen, Subnormal operators in strictly cyclic operator algebras, Pacific J. Math. 49 (1973), 7-11. MR 0355670 (50:8144)
2.: K. Davidson, Nest Algebras, Pitman Research Notes in Mathematics Series 191 (Longman Scientific and Technical, 1988). MR 972978 (90f:47062)
3.: J. Froelich, B. Mathes, Bi-strictly cyclic operators, New York J. Math. 1 (1995), 97-110. MR 1323805 (96h:47009)
4.: J. A. Erdos, The commutant of the Volterra operator, Integral Equations Operator Theory 5 (1982), 127-130 MR 646883 (83i:47040)
5.: D. A. Herrero, Operator algebras of finite strict multiplicity, Indiana Univ. Math. J. 22 (1972), 13-24. MR 0315468 (47:4017)
6.: D. A. Herrero, Operator algebras of finite strict multiplicity. II, Indiana Univ. Math. J. 27 (1978), 9-18. MR 475718 (81g:47048)
7.: D. A. Herrero, D. R. Larson, W. R. Wogen, Semitriangular operators, Houston J. Math. 17 (1991), 477-499. MR 1147270 (92m:47037)
8.: E. Hewitt, K. Stromberg, Real and Abstract Analysis, Graduate Texts in Mathematics 25, Springer-Verlag, 1965. MR 0367121 (51:3363)
9.: A. Lambert, Strictly Cyclic Operator Algebras, Dissertation, University of Michigan, Ann Arbor, Mich., 1970.
10.: A. Lambert, Strictly cyclic operator algebras, Pacific J. Math. 39 (1971), 717-726. MR 0310664 (46:9762)
11.: C. Rickart, General Theory of Banach Algebras, The University Series in Higher Mathematics, Van Nostrand, 1960. MR 0115101 (22:5903)
12.: D. Sarason, Invariant Subspaces, Topics in Operator Theory, Math. Surveys, no. 13, Amer. Math. Soc., Providence, R.I., 1974. MR 0358396 (50:10862)
13.: D. Sarason, Generalized interpolation in $H^\infty$ , Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 0208383 (34:8193)
14.: A. Shields,Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, no. 13, Amer. Math. Soc., Providence, R.I., 1974. MR 0361899 (50:14341)
15.: R. E. Waterman, Invariant subspaces, similarity and isometric equivalence of certain commuting operators in , Pacific J. Math. 48 (1973), 593-613. MR 0399894 (53:3735)
16.: W. R. Wogen, Some counterexamples in nonselfadjoint algebras, Ann. of Math. (2) 126 (1987), 415-427. MR 908152 (89b:47066)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B28, 47L50, 46L07, 46H10

Retrieve articles in all Journals with MSC (2000): 46B28, 47L50, 46L07, 46H10

Additional Information:

Ben Mathes
Affiliation: Department of Mathematics, Colby College, Waterville, Maine 04963
Email: dbmathes@colby.edu

DOI: 10.1090/S0002-9939-09-09938-9
PII: S 0002-9939(09)09938-9
Keywords: Strictly cyclic algebra, strictly cyclic operators, large point spectrum
Received by editor(s): April 29, 2008,
Received by editor(s) in revised form: February 20, 2009
Posted: May 28, 2009
Dedicated: Dedicated to Don Hadwin
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|