Non Approximately Inner Tensor Product of C*—Algebras

Authors: Rasoul Abazari

Abstract:

In this paper, we show that C*-tensor product of an arbitrary C*-algebra A, (not unital necessary) and C*-algebra B without ground state, have no approximately inner strongly continuous one-parameter group of *-automorphisms.

Keywords: One–parameter group, C*– tensor product, Approximately inner, Ground state.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335046

References:

[1] Niknam. A, Infinitesimal generators of C* —Algebras, Potential Analysis, 6 (1997) 1-9.
[2] Lance.E.0 and Niknam. A,Unbounded derivations of group C*— Algebras, Proc. Amer.math.Soc. 61 (2) (1976) 310-314.
[3] Powers. R.T and Sakai.S, Existence of ground states and KMS states for approximately inner dynamics , commun.math.Phys, 39 (1975) 273-288.
[4] Ruelle. 0, commun.math.Phys, 11 (1969) 339-345.
[5] Robinson. D.W,I: commun.math.Phys, 6 (1967) 151-160. II: commun.math.Phys, 7 (1968) 337-348.
[6] Ruelle. 0, Statistical mechanics, New York, W.A. Benjamin, Ins 1969.
[7] Dunford. N and Schwartz.J.T, Linear operators, part I. New York: Interscience pub. 1963.