Let H be a separable infinite dimensional Hilbert space, and let T_1 be the the family of all trace class operators on H. The purpose of this paper is to establish a number of equivalent conditions which characterize the trace among the bounded linear functionals on T_1.

Contents
1 Introduction ...................1
2 Preliminaries ..................2
3 Main Results ...................3
4 Concluding Remarks ............18
5 Reference .....................19

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