Generalized stieltjes integrals and a strong representation theorem for continuous linear maps on a function space

1969 ◽  
Vol 182 (1) ◽  
pp. 60-66 ◽  
Author(s):  
David J. Uherka
Keyword(s):  
Function Space ◽  
Representation Theorem ◽  
Continuous Linear ◽  
Linear Maps ◽  
Strong Representation

A completeness theorem for higher order logics

2000 ◽  
Vol 65 (2) ◽  
pp. 857-884 ◽  
Author(s):  
Gábor Sági
Keyword(s):  
Set Theory ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Higher Order ◽  
Algebraic Solution ◽  
Algebraic Proof ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Strong Representation ◽  
Algebraic Counterpart

AbstractHere we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.

Continuous Linear Maps

2014 ◽  
pp. 115-138
Author(s):  
Joseph Muscat
Keyword(s):  
Continuous Linear ◽  
Linear Maps

scholarly journals The second dual of C0 (S, A)

1994 ◽  
Vol 56 (3) ◽  
pp. 303-313
Author(s):  
Stephen T. L. Choy ◽  
James C. S. Wong
Keyword(s):  
Function Space ◽  
Simple Proof ◽  
Representation Theorem ◽  
Generalized Functions ◽  
Arens Product ◽  
Nikodym Property ◽  
Second Dual ◽  
Vector Valued Function ◽  
Vector Valued

AbstractThe second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.

scholarly journals On the surjectivity of linear maps on locally convex spaces

1982 ◽  
Vol 32 (2) ◽  
pp. 187-211 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Basic Notion ◽  
Linear Map ◽  
Linear Maps ◽  
Locally Convex ◽  
Do So ◽  
Convex Spaces

AbstractThe aim of this note is to investigate the structure of general surjectivity problem for a continuous linear map between locally convex spaces. We shall do so by using the method introduced in Yamamuro (1980). Its basic notion is that of calibrations which has been introduced in Yamamuro (1975), studied in detail in Yamamuro (1979) and appliced to several problems in Yamamuro (1978) and Yamamuro (1979a).

Spectral representation of linear transformations in ω

1951 ◽  
Vol 47 (3) ◽  
pp. 461-472 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Representation Theorem ◽  
Spectral Representation ◽  
Complex Numbers ◽  
General Description ◽  
Continuous Linear ◽  
Linear Transformations ◽  
Usual Topology

1. In this paper we consider the following problems, for continuous linear transformations in the space ω, whose points are arbitrary sequences of complex numbers, with the usual topology:(a) the establishment of a spectral representation theorem; and(b) the general description of the spectrum.

STRONG REPRESENTATION OF A DISCRETE DECISION PROCESS BY POSITIVELY/NEGATIVELY BITONE SEQUENTIAL DECISION PROCESS

2007 ◽  
Vol 24 (02) ◽  
pp. 181-202
Author(s):  
YUKIHIRO MARUYAMA
Keyword(s):  
Representation Theorem ◽  
Decision Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sequential Decision ◽  
Sequential Decision Process ◽  
Strong Representation ◽  
Necessary And Sufficient

In this paper, we will introduce a new subclass of bitone sequential decision process (bsdp) and give a representation theorem for the subclass called positively/negatively bsdp, shortly, p/n bsdp, that is, necessary and sufficient condition for p/n bsdp to strongly represent a given discrete decision process (ddp).

scholarly journals Pitt's theorem for operators between general Lorentz sequence spaces

2002 ◽  
Vol 90 (1) ◽  
pp. 101 ◽  
Author(s):  
J. A. López Molina
Keyword(s):  
Sequence Spaces ◽  
Continuous Linear ◽  
Linear Maps ◽  
Pitt’S Theorem

We characterize the pairs of general Lorentz sequence spaces $\ell^{u,v}(\nu),$ $\ell^{p,q}(\mu), 0 < u, v, p, q < \infty$ such that all continuous linear maps from the first space into the second one are compact.

scholarly journals Closed linear maps from a barrelled normed space into itself need not be continuous

1998 ◽  
Vol 57 (2) ◽  
pp. 177-179 ◽  
Author(s):  
José Bonet
Keyword(s):  
Normed Space ◽  
Continuous Linear ◽  
Closed Graph ◽  
Linear Map ◽  
Linear Maps ◽  
Barrelled Spaces

Examples of normed barrelled spacesEor quasicomplete barrelled spacesEare given such that there is a non-continuous linear map from the spaceEinto itself with closed graph.

Symmetrically Completely Bounded Linear Maps Between C*-Algebras

1992 ◽  
Vol 35 (2) ◽  
pp. 278-286
Author(s):  
Wai-Shing Tang
Keyword(s):  
Hilbert Space ◽  
Representation Theorem ◽  
Linear Subspace ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
C Algebras ◽  
New Class ◽  
Linear Maps

AbstractWe study the properties of a new class SCB(L, B) of bounded linear maps, called symmetrically completely bounded maps, from a linear subspace L of a C* -algebra to another C*-algebra B. This class contains the class of all completely bounded linear maps from L to B. In particular, we obtain a representation theorem for maps in SCB(L, B) when B is the algebra of all bounded linear operators on a Hilbert space.

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