scholarly journals Analytic Functionals on a Countably Infinite Dimensional Topological Vector Space

1980 ◽  
Vol 03 (2) ◽  
pp. 271-289 ◽  
Author(s):  
Yoshihisa FUJIMOTO
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Infinite Dimensional ◽  
Analytic Functionals ◽  
Countably Infinite

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 Recursive equivalence types of vector spaces

1974 ◽  
Vol 18 (3) ◽  
pp. 376-384 ◽  
Author(s):  
Alan G. Hamilton
Keyword(s):  
Vector Space ◽  
Vector Spaces ◽  
Natural Numbers ◽  
Infinite Dimensional ◽  
Recursively Enumerable ◽  
Countably Infinite

We consider subspaces of a vector space UF, which is countably infinite dimensional over a recursively enumerable field F with recursive operations, where the operations in UF are also recursive, and where, of course, F and UF are sets of natural numbers. It is the object of this paper to investigate recursive equivalence types of such vector spaces and the ways in which their properties are analogous to and depend on properties of recursive equivalence types of sets.

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.

Bases and α-dimensions of countable vector spaces with recursive operations

1970 ◽  
Vol 35 (1) ◽  
pp. 85-96
Author(s):  
Alan G. Hamilton
Keyword(s):  
Vector Space ◽  
Vector Spaces ◽  
Natural Numbers ◽  
Infinite Dimensional ◽  
Recursively Enumerable ◽  
Countably Infinite

This paper is based on the notions originally described by Dekker [2], [3], and the reader is referred to these for explanation of notation etc. Briefly, we are concerned with a countably infinite dimensional countable vector space Ū with recursive operations, regarded as being coded as a set of natural numbers. Necessarily, then, Ū must be a vector space over a field which itself is in some sense recursively enumerable and has recursive operations.

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

scholarly journals Polynomial ring representations of endomorphisms of exterior powers

2021 ◽  
Author(s):  
Ommolbanin Behzad ◽  
André Contiero ◽  
Letterio Gatto ◽  
Renato Vidal Martins
Keyword(s):  
Lie Algebra ◽  
Polynomial Ring ◽  
Vertex Operators ◽  
Exterior Power ◽  
Infinite Dimensional ◽  
Symmetric Structure ◽  
Rational Polynomials ◽  
Exterior Powers ◽  
Vertex Representation ◽  
Countably Infinite

AbstractAn explicit description of the ring of the rational polynomials in r indeterminates as a representation of the Lie algebra of the endomorphisms of the k-th exterior power of a countably infinite-dimensional vector space is given. Our description is based on results by Laksov and Throup concerning the symmetric structure of the exterior power of a polynomial ring. Our results are based on approximate versions of the vertex operators occurring in the celebrated bosonic vertex representation, due to Date, Jimbo, Kashiwara and Miwa, of the Lie algebra of all matrices of infinite size, whose entries are all zero but finitely many.

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