Norm-Additive Maps on the Positive Definite Cone of a $$\varvec{C^{*}}$$ C ∗ -Algebra

作者: Marcell Gaál

DOI: 10.1007/S00025-018-0916-4

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摘要: In this paper, we determine the structure of Schatten p-norm additive maps on set positive invertible elements a $$C^{*}$$ -algebra carrying faithful normalized trace. It turns out that any such transformation originates from Jordan $$^*$$ -isomorphism underlying -algebra. fact, our result can be viewed as characterization sort isomorphisms.

参考文章(16)
Lajos Molnár, Patrícia Szokol, Transformations Preserving Norms of Means of Positive Operators and Nonnegative Functions Integral Equations and Operator Theory. ,vol. 83, pp. 271- 290 ,(2015) , 10.1007/S00020-015-2241-6
Jacques Dixmier, Von Neumann Algebras ,(1981)
Maliheh Hosseini, Juan J. Font, Real-Linear Isometries and Jointly Norm-Additive Maps on Function Algebras Mediterranean Journal of Mathematics. ,vol. 13, pp. 1933- 1948 ,(2016) , 10.1007/S00009-015-0607-2
Maliheh Hosseini, Juan J. Font, Norm-additive in modulus maps between function algebras Banach Journal of Mathematical Analysis. ,vol. 8, pp. 79- 92 ,(2014) , 10.15352/BJMA/1396640053
Thierry Fack, Hideki Kosaki, Generalized s-numbers of τ-measurable operators Pacific Journal of Mathematics. ,vol. 123, pp. 269- 300 ,(1986) , 10.2140/PJM.1986.123.269
Edward Nelson, Notes on non-commutative integration Journal of Functional Analysis. ,vol. 15, pp. 103- 116 ,(1974) , 10.1016/0022-1236(74)90014-7
Thomas Tonev, Rebekah Yates, Norm-linear and norm-additive operators between uniform algebras Journal of Mathematical Analysis and Applications. ,vol. 357, pp. 45- 53 ,(2009) , 10.1016/J.JMAA.2009.03.039
Gergő Nagy, Preservers for the -Norm of Linear Combinations of Positive Operators Abstract and Applied Analysis. ,vol. 2014, pp. 1- 9 ,(2014) , 10.1155/2014/434121
Osamu Hatori, Go Hirasawa, Takeshi Miura, Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras Open Mathematics. ,vol. 8, pp. 597- 601 ,(2010) , 10.2478/S11533-010-0025-4
M. ESHAGHI GORDJI, n -JORDAN HOMOMORPHISMS Bulletin of The Australian Mathematical Society. ,vol. 80, pp. 159- 164 ,(2009) , 10.1017/S000497270900032X