Proceedings of the American Mathematical Society

Author(s): Fernanda Botelho; James Jamison
Journal: Proc. Amer. Math. Soc. 136 (2008), 1397-1402.
MSC (2000): Primary 47A65; Secondary 47B15, 47B37
Posted: November 28, 2007
Retrieve article in: PDF

Abstract: We characterize generalized bi-circular projections on $\mathcal{I}(\mathcal{H}),$ a minimal norm ideal of operators in $\mathcal{B}(\mathcal{H}),$ where $\mathcal{H}$ is a separable infinite dimensional Hilbert space.

18.: Behrends, E., M-Structure and the Banach-Stone Theorem, Lecture Notes in Mathematics 736 (1979), Springer-Verlag. MR 547509 (81b:46002)
1.: Berkson, E., Hermitian projections and orthogonality in Banach spaces, Proc. London Math. Soc. 24:3 (1972), 101-118. MR 0295123 (45:4191)
2.: Bernau, S. J. and Lacey, H. E., Bicontractive projections and reordering of spaces, Pac. Journal of Math. 69:2 (1977), 291-302. MR 0487416 (58:7054)
3.: Botelho, F. and Jamison, J. E., Generalized bi-circular projections on $\mathcal{C}(\Omega, X)$ , Rocky Mountain Journal (to appear).
4.: Friedman, Y. and Russo, B., Contractive projections on , Transactions of the AMS 273:1 (1982), 57-73. MR 664029 (83i:46062)
5.: Fleming, R. and Jamison, J., Isometries on Banach Spaces (2003), Chapman & Hall.
6.: Fosner, M.,Ilisevic, D. and Li, C., G-invariant norms and bicircular projections, Linear Algebra and Applications 420 (2007), 596-608. MR 2278235
7.: Groot, J. and Wille, R., Rigid continua and topological group-pictures, Arch. Math. IX (1958), 441-446. MR 0101514 (21:324)
8.: Jamison, J. E., Bicircular projections on some Banach spaces, Linear Algebra and Applications 420 (2007), 29-33. MR 2277626
9.: Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces I (1977), Springer Verlag. MR 0500056 (58:17766)
10.: Shatten, R., Norm Ideals of Completely Continuous Operators (1970), Springer-Verlag, Berlin. MR 0257800 (41:2449)
11.: Sourour, A. R., Isometries of norm ideals of compact operators, J. Funct. Anal. 43 (1981), 69-77. MR 639798 (84e:47061)
12.: Spain, P. G., Ultrahermitian projections on Banach spaces, preprint (2006).
13.: Taylor, A. E., Introduction to Functional Analysis (1957), John Wiley & Sons Inc. MR 0098966 (20:5411)
14.: Fong, C. K. and Sourour, A. R., On the operator identity $\sum A_kXB_k = 0,$ Can. J. Math., XXXI (1979), 845-857. MR 540912 (80h:47020)
15.: Randrianantoanina, B., Norm-One projections in Banach spaces, Taiwanese Journal of Mathematics. 5:1 (2001), 35-95. MR 1816130 (2003d:46001)
16.: Stachó, L. L. and Zalar, B., Bicircular projections on some matrix and operator spaces, Linear Algebra and Applications 384 (2004), 9-20. MR 2055340 (2005a:46146)
17.: Stachó, L. L. and Zalar, B., Bicircular projections and characterization of Hilbert spaces, Proc. Amer. Math. Soc. 132 (2004), 3019-3025. MR 2063123 (2005b:46152)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A65, 47B15, 47B37

Fernanda Botelho
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Email: mbotelho@memphis.edu

James Jamison
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Email: jjamison@memphis.edu

DOI: 10.1090/S0002-9939-07-09134-4
PII: S 0002-9939(07)09134-4
Keywords: Isometry, generalized bi-circular projections, Banach spaces, ideals of operators
Received by editor(s): October 16, 2006
Received by editor(s) in revised form: February 15, 2007
Posted: November 28, 2007
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS