scholarly journals The Lebesgue decomposition theorem for partially ordered semigroup-valued measures

1978 ◽  
Vol 71 (2) ◽  
pp. 207-207 ◽  
Author(s):  
Panaiotis K. Pavlakos
Keyword(s):  
Decomposition Theorem ◽  
Ordered Semigroup ◽  
Lebesgue Decomposition ◽  
Partially Ordered

scholarly journals Continued fractions built from convex sets and convex functions

2015 ◽  
Vol 17 (05) ◽  
pp. 1550003 ◽  
Author(s):  
Ilya Molchanov
Keyword(s):  
Convex Functions ◽  
Continued Fractions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Ordered Semigroup ◽  
Minkowski Addition ◽  
Partially Ordered ◽  
The Family ◽  
Sufficient Conditions For Convergence

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalization of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

scholarly journals Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups

1981 ◽  
Vol 31 (3) ◽  
pp. 325-336 ◽  
Author(s):  
D. B. Mcalister
Keyword(s):  
Partial Order ◽  
Local Structure ◽  
Structure Theorem ◽  
Main Tool ◽  
Natural Partial Order ◽  
Ordered Semigroup ◽  
Ordered Group ◽  
Partially Ordered ◽  
Rees Matrix Semigroups ◽  
Matrix Semigroups

AbstractA partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that {} has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.

The Arithmetic of the Quasi-Uniserial Semigroups without Zero

1971 ◽  
Vol 23 (3) ◽  
pp. 507-516 ◽  
Author(s):  
Ernst August Behrens
Keyword(s):  
Simple Semigroup ◽  
Disjoint Union ◽  
Maximal Subgroups ◽  
Ordered Semigroup ◽  
Partially Ordered ◽  
Completely Simple Semigroup ◽  
Image Position ◽  
Previous Paragraph ◽  
Completely Simple ◽  
Identity Elements

An element a in a partially ordered semigroup T is called integral ifis valid. The integral elements form a subsemigroup S of T if they exist. Two different integral idempotents e and f in T generate different one-sided ideals, because eT = fT, say, implies e = fe ⊆ f and f = ef ⊆ e.Let M be a completely simple semigroup. M is the disjoint union of its maximal subgroups [4]. Their identity elements generate the minimal one-sided ideals in M. The previous paragraph suggests the introduction of the following hypothesis on M.Hypothesis 1. Every minimal one-sided ideal in M is generated by an integral idempotent.

scholarly journals LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS

2015 ◽  
Vol 58 (2) ◽  
pp. 491-501 ◽  
Author(s):  
ZSIGMOND TARCSAY
Keyword(s):  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Absolutely Continuous ◽  
Hermitian Forms ◽  
Lebesgue Type Decomposition ◽  
Representable Functional ◽  
Type Decomposition

AbstractWe offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.

scholarly journals A wide Perron integral

1986 ◽  
Vol 34 (2) ◽  
pp. 233-251
Author(s):  
D. N. Sarkhel
Keyword(s):  
Decomposition Theorem ◽  
Mean Value ◽  
Lebesgue Decomposition ◽  
Integration By Parts ◽  
Mean Value Theorems ◽  
Limit Process ◽  
Real Functions ◽  
Marcinkiewicz Theorem ◽  
Perron Integral ◽  
Interesting Generalization

In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.

scholarly journals The Quantifier Semigroup for Bipartite Graphs

10.37236/610 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Leonard J. Schulman
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
The Other ◽  
Monotone Mappings ◽  
Ordered Semigroup ◽  
Partially Ordered

In a bipartite graph there are two widely encountered monotone mappings from subsets of one side of the graph to subsets of the other side: one corresponds to the quantifier "there exists a neighbor in the subset" and the other to the quantifier "all neighbors are in the subset." These mappings generate a partially ordered semigroup which we characterize in terms of "run-unimodal" words.

A Lebesgue Decomposition Theorem for C* Algebras

1972 ◽  
Vol 15 (1) ◽  
pp. 87-91 ◽  
Author(s):  
Michael Henle
Keyword(s):  
Absolute Continuity ◽  
Linear Functional ◽  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
C Algebras ◽  
Positive Linear Functional ◽  
Decomposition Theorems

This paper, by generalizing von Neumann's proof of the Radon-Nikodym and Lebesgue decomposition theorems [3], obtains analogous results for positive linear functional on a C* algebra. The concept of "absolute continuity" used and the Radon-Nikodym portion of the resulting theorem are due to Dye [2].

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