ON σ-FINITE INTEGRALS ON C-ALGEBRAS

This paper considers positive Iinear functionals f defined on a dense -subalgebra, which is an analogue of the continuous functions with compact supports, of a C_*-algebra. L~1-spaces associated with f are studied. Also introduced is an analogue of the bounded Borel functions vanishing at infinity.     

Hilbert C*模及其有界模映射

设E为C^*代数A上可数生成的Hilbert模,B(E)为E上有界模映射全体,则B(E)保距同构于K(E)的左乘子,其中K(E)为E上“紧”模映射全体。当A为无限维本原C^*代数且E为自对偶模,则E为代数有限生成。     

INVARIANT SUBSPACES AND EIGEVALUES OF ELEMENTS IN C-ALGEBRAS

Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.