JOURNAL BROWSE
Search
Advanced SearchSearch Tips
MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS
MABROUK, MOHAMED;
  PDF(new window)
 Abstract
Let and be two unital -algebras. Denote by W(a) the numerical range of an element . We show that the condition W(ax) = W(bx), implies that a = b. Using this, among other results, it is proved that if : is a surjective map such that for all a, b and , then and the map is multiplicative.
 Keywords
-algebras;numerical range;preserving the numerical range;
 Language
English
 Cited by
1.
Numerical radius characterizations of elements in -algebras, Linear and Multilinear Algebra, 2017, 1  crossref(new windwow)
 References
1.
R. An and J. Hou, Additivity of Jordan multiplicative maps on Jordan operator algebras, Taiwanese J. Math. 10 (2006), no. 1, 45-64.

2.
F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and elements of normed algebras, Cambridge Univ. Press, London, 1971.

3.
M. Bresar and S. Spela, Determining elements in Banach algebras through spectral properties, J. Math. Anal. Appl. 393 (2012), no. 1, 144-150. crossref(new window)

4.
J. T. Chan, Numerical radius preserving operators on B(H), Proc. Amer. Math. Soc. 123 (1995), no. 5, 1437-1439.

5.
M. A. Chebotar, W. F. Ke, P. K. Lee, and N. C. Wong, Mappings preserving zero products, Studia Math. 155 (2003), no. 1, 77-94. crossref(new window)

6.
J. B. Conway, A Course in Functional Analysis, Springer, 1990.

7.
H. L. Gau and C. K. Li, C*-isomorphisms, Jordan isomorphisms, and numerical range preserving maps, Proc. Amer. Math. Soc. 135 (2007), no. 9, 2907-2914. crossref(new window)

8.
P. R. Halmos, A Hilbert Space Problem Book, 2nd ed., Springer, New York, 1982.

9.
J. Hou and Q. Di, Maps preserving numerical ranges of operator products, Proc. Amer. Math. Soc. 134 (2006), no. 5, 1435-1446.

10.
R. V. Kadisson, Isometries of operator algebras, Ann. of Math. 54 (1951), no. 2, 325- 338. crossref(new window)

11.
E. C. Lance, Unitary operators on Hilbert C*-modules, Bull. London Math. Soc. 4 (1994), no. 4, 363-366.

12.
C. K. Li, A survey on linear preservers of numerical ranges and radii, Taiwanese J. Math. 5 (2001), no. 3, 477-496.

13.
C. K. Li and E. Poon, Maps preserving the joint numerical radius distance of operators, Linear Algebra Appl. 437 (2012), no. 5, 1194-1204. crossref(new window)

14.
L. Molnar, On isomorphisms of standard operator algebras, Studia Math. 142 (2000), no. 3, 295-302.

15.
V. Pellegrini, Numerical range preserving operators on a Banach algebra, Studia Math. 54 (1975), no. 2, 143-147. crossref(new window)

16.
J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a Banach algebras, Tohoku Math. J. 20 (1968), 417-424. crossref(new window)