Weighted inductive and projective limits of normed Köthe function spaces

1988 ◽  
Vol 13 (1-2) ◽  
pp. 147-161 ◽  
Author(s):  
Konrad Reiher
Keyword(s):  
Function Spaces ◽  
Inductive And Projective 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.

INDUCTIVE AND PROJECTIVE LIMITS OF COVERING k-GROUPS OF n-GROUPS

1984 ◽  
Vol 17 (1) ◽  
Author(s):  
Jacek Michalski
Keyword(s):  
Inductive And Projective Limits ◽  
Projective Limits

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 On bases in strict inductive and projective limits of locally convex spaces

1985 ◽  
Vol 119 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Klaus Floret ◽  
V. B. Moscatelli
Keyword(s):  
Locally Convex Spaces ◽  
Inductive And Projective Limits ◽  
Projective Limits ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Inductive and projective limits of normed spaces

1968 ◽  
Vol 9 (2) ◽  
pp. 103-105 ◽  
Author(s):  
John S. Pym
Keyword(s):  
Inductive Limit ◽  
Vector Spaces ◽  
Continuous Linear ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Inductive System ◽  
Linear Maps ◽  
Inductive And Projective Limits ◽  
Projective Limits ◽  
Locally Convex

Let {Ui, Uij} be an inductive system of normed linear spaces Ui and continuous linear maps uij; Uj → Ui. (We write j ≺ i if uij: Uj → Ui.) An inductive limit of the system with respect to a class of spaces A in and maps f in is a space Uu in Uu and a system ui → Uu of maps in such that (i) whenever j ≺ i, and that (ii) if A is any space in and fi: Ui → A is any system of maps in for which then there is a unique map f: Uu → A in such that fi = fo ui for each i. If is the class of all vector spaces and is the class of linear maps, we obtain the algebraic inductive limit, which we denote simply by U. The usual choice is to take to be the class of locally convex spaces and the class of continuous linear maps; the inductive limit UL then always exists [1, § 16 C]. If is again the continuous linear mappings but contains only normed spaces, the corresponding inductive limit UN may not always exist. However, if in addition we require that contains just contractions (norm-decreasing linear mappings), then an inductive limit Uc will exist if every uij is a contraction [2]. We shall give a condition under which these limits coincide (as far as possible), and consider the corresponding condition for projective limits.

scholarly journals Inductive and projective limits of smooth topological vector spaces

1972 ◽  
Vol 6 (2) ◽  
pp. 227-240 ◽  
Author(s):  
John W. Lloyd ◽  
S. Yamamuro
Keyword(s):  
General Theory ◽  
Banach Spaces ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Inductive And Projective Limits ◽  
Nuclear Spaces ◽  
Projective Limits ◽  
The Relationship

In J. Math. Mech. 15 (1966), 877–898, Bonic and Frampton have laid the foundation for a general theory of smoothness of Banach spaces. In this paper, we shall study one aspect of the smoothness of topological vector spaces, namely, the relationship between smoothness and inductive and protective limits of topological vector spaces. As a consequence, we obtain smoothness results for nuclear spaces and some Montei spaces.

Function spaces between crystal space and Fourier-transform space

1959 ◽  
Vol 112 (1-6) ◽  
pp. 22-32 ◽  
Author(s):  
A. L. Patterson
Keyword(s):  
Fourier Transform ◽  
Function Spaces ◽  
Crystal Space

Function Spaces and Nonsymmetric Norm Preserving Maps

2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  
Function Spaces

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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