Conditions for certain forms of completeness in the class of projective limits of sequences of inductive limits of sequences of Fr�chet spaces

1977 ◽  
Vol 11 (1) ◽  
pp. 82-83 ◽  
Author(s):  
E. T. Shavgulidze
Keyword(s):  
Inductive Limits ◽  
Projective Limits

Inductive Limits and Projective Limits of Groups

2010 ◽  
pp. 379-381
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Michel Coornaert
Keyword(s):  
Inductive Limits ◽  
Projective Limits

Lifting Inductive and Projective Limits

1967 ◽  
Vol 19 ◽  
pp. 1329-1339 ◽  
Author(s):  
Johann Sonner
Keyword(s):  
Inductive Limits ◽  
Inductive And Projective Limits ◽  
Projective Limits ◽  
Universal Solutions

In this paper, which is the fourth in a series of articles (11, 12, 13) on universal solutions in categories, a relationship between inductive limits and final structures (or projective limits and initial structures) is studied. The problems to be encountered are illustrated by the following example.

scholarly journals Использование гомологических методов на базе итерированных спектров в функциональном анализе

2012 ◽  
Author(s):  
E.I. Smirnov
Keyword(s):  
Locally Convex Spaces ◽  
Closed Graph ◽  
Closed Graph Theorem ◽  
Inductive Limits ◽  
Quotient Spaces ◽  
New Concepts ◽  
Inductive And Projective Limits ◽  
Projective Limits ◽  
Locally Convex ◽  
Convex Spaces

We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or H-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular H-limit are projective and inductive limits of separated locally convex spaces. The class of H-spaces contains Frechet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quotient spaces. Moreover, for H-space an unproved variant of the closed graph theorem holds true. Homological methods are used for proving of theorems of vanishing at zero for first derivative of Hausdorff limit functor: Haus1(X)=0.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

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].

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

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.

scholarly journals *—Inductive limits and partition of unity

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.

Projective Limits of Finite-Dimensional Lie Groups

2003 ◽  
Vol 87 (03) ◽  
pp. 647-676 ◽  
Author(s):  
Karl H. Hofmann ◽  
Sidney A. Morris
Keyword(s):  
Lie Groups ◽  
Finite Dimensional ◽  
Projective Limits
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