Generalized Inductive Limits and Quasidiagonality

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

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Strictly barrelled disks in inductive limits of quasi-(LB)-spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171296001007 ◽

1996 ◽

Vol 19 (4) ◽

pp. 727-732

Author(s):

Carlos Bosch ◽

Thomas E. Gilsdorf

Keyword(s):

Convex Space ◽

Inductive Limit ◽

Linear Span ◽

Locally Convex Space ◽

Minkowski Functional ◽

Closed Graph ◽

Inductive Limits ◽

Locally Convex ◽

Barrelled Space

A strictly barrelled diskBin a Hausdorff locally convex spaceEis a disk such that the linear span ofBwith the topology of the Minkowski functional ofBis a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi-(LB)-space is bounded. It is shown that a locally strictly barrelled quasi-(LB)-space is locally complete. Also, we show that a regular inductive limit of quasi-(LB)-spaces is locally complete if and only if each closed bounded disk is a strictly barrelled disk in one of the constituents.

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*—Inductive limits and partition of unity

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171289000529 ◽

1989 ◽

Vol 12 (3) ◽

pp. 429-434

Author(s):

V. Murali

Keyword(s):

Inductive Limit ◽

Partition Of Unity ◽

Vector Spaces ◽

Inductive Limits ◽

Topological Vector Spaces ◽

Limit Space ◽

Direct Sum

In this note we define and discuss some properties of partition of unity on *-inductive limits of topological vector spaces. We prove that if a partition of unity exists on a *-inductive limit space of a collection of topological vector spaces, then it is isomorphic and homeomorphic to a subspace of a *-direct sum of topological vector spaces.

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