scholarly journals Hypocontinuity of multiplication on the Clifford algebra of an infinite-dimensional topological vector space

1975 ◽  
Vol 50 (1) ◽  
pp. 435-435
Author(s):  
Robert A. Haberstroh
Keyword(s):  
Vector Space ◽  
Clifford Algebra ◽  
Topological Vector Space ◽  
Infinite Dimensional

scholarly journals On a Semigroup Problem II

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1392
Author(s):  
Viorel Nitica ◽  
Andrew Torok
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Infinite Dimensional ◽  
Finite Dimensional

We consider the following semigroup problem: is the closure of a semigroup S in a topological vector space X a group when S does not lie on “one side” of any closed hyperplane of X? Whereas for finite dimensional spaces, the answer is positive, we give a new example of infinite dimensional spaces where the answer is negative.

scholarly journals On properly separable quotients of strict (LF) Spaces

1989 ◽  
Vol 47 (2) ◽  
pp. 307-312 ◽  
Author(s):  
W. J. Robertson
Keyword(s):  
Vector Space ◽  
Banach Spaces ◽  
Topological Vector Space ◽  
Inductive Limit ◽  
General Question ◽  
Fréchet Spaces ◽  
Infinite Dimensional

AbstractAll known Banach spaces have an infinite-dimensional separable quotient and so do all nonnormable Fréchet spaces, although the general question for Banach spaces is still open. A properly separable topological vector space is defined, in such a way that separable and properly separable are equivalent for an infinite-dimensional complete metrisable space. The main result of this paper is that the strict inductive limit of a sequence of non-normable Fréchet spaces has a properly separable quotient.

scholarly journals Linearization of certain uniform homeomorphisms

2007 ◽  
Vol 82 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Anthony Weston
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Banach Spaces ◽  
Topological Vector Space ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Infinite Dimensional

AbstractThis article concerns the uniform classification of infinite dimensional real topological vector spaces. We examine a recently isolated linearization procedure for uniform homeomorphisms of the form φ: X →Y, where X is a Banach space with non-trivial type and Y is any topological vector space. For such a uniform homeomorphism φ, we show that Y must be normable and have the same supremal type as X. That Y is normable generalizes theorems of Bessaga and Enflo. This aspect of the theory determines new examples of uniform non-equivalence. That supremal type is a uniform invariant for Banach spaces is essentially due to Ribe. Our linearization approach gives an interesting new proof of Ribe's result.

Probability Measures with Big Kernels

2001 ◽  
Vol 8 (2) ◽  
pp. 333-346
Author(s):  
Nguyen Duy Tien ◽  
V. Tarieladze
Keyword(s):  
Probability Measure ◽  
Vector Space ◽  
Topological Vector Space ◽  
Dual Space ◽  
Full Measure ◽  
Probability Measures ◽  
Infinite Dimensional ◽  
Cylindrical Measure ◽  
Second Category

Abstract It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [Kernel associated with a cylindrical measure, Springer-Verlag, 1981, p. 69] is solved by proving that the annihilator of the kernel of a measure μ coincides with the annihilator of μ if and only if the topology of μ-convergence in the dual space is essentially dually separated.

On Semi - Pre irresolute Topological Vector Space

2018 ◽  
Vol 14 (3) ◽  
pp. 184-192
Author(s):  
Radhi Ali ◽  
◽  
Jalal Hussein Bayati ◽  
Suhad Hameed
Keyword(s):  
Vector Space ◽  
Topological Vector Space

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

scholarly journals A class of factorable topological algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 53-59 ◽  
Author(s):  
E. Ansari-Piri
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Approximate Identity ◽  
Necessary Condition ◽  
Topological Algebras ◽  
Approximate Identities ◽  
Cohen Factorization ◽  
Locally Convex ◽  
Space Property ◽  
Uniformly Bounded

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

Sign in / Sign up

Export Citation Format

Share Document