scholarly journals ON THE ORDER STRUCTURE OF REPRESENTABLE FUNCTIONALS

2017 ◽  
Vol 60 (2) ◽  
pp. 289-305 ◽  
Author(s):  
ZSIGMOND TARCSAY ◽  
TAMÁS TITKOS
Keyword(s):  
Operator Algebras ◽  
Extreme Points ◽  
Positive Operators ◽  
Order Structure ◽  
Sufficient Condition ◽  
Lebesgue Decomposition ◽  
Decomposition Theory ◽  
The One ◽  
Order Intervals ◽  
Complete Analogy

AbstractThe main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.

Extreme Points in Quotients of Operator Algebras

1988 ◽  
pp. 67-91
Author(s):  
Kenneth R. Davidson ◽  
Timothy G. Feeman ◽  
Allen L. Shields
Keyword(s):  
Operator Algebras ◽  
Extreme Points

Extensions of positive operators and extreme points. I

1979 ◽  
Vol 42 (1) ◽  
pp. 279-284 ◽  
Author(s):  
Z. Lipecki ◽  
D. Plachky ◽  
W. Thomsen
Keyword(s):  
Extreme Points ◽  
Positive Operators

Products of Decomposable Positive Operators

1994 ◽  
Vol 46 (4) ◽  
pp. 854-871 ◽  
Author(s):  
Terrance Quinn
Keyword(s):  
Operator Algebras ◽  
Positive Operators ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Direct Integral ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Decomposable Operators

AbstractIn recent years there has been a growing interest in problems of factorization for bounded linear operators. We first show that many of these problems properly belong to the category of C*-algebras. With this interpretation, it becomes evident that the problem is fundamental both to the structure of operator algebras and the elements therein. In this paper we consider the direct integral algebra with separable and infinite dimensional. We generalize a theorem of Wu (1988) and characterize those decomposable operators which are products of non-negative decomposable operators. We do this by first showing that various results on operator ranges may be generalized to “measurable fields of operator ranges”.

Leibniz on Apperception and Animal Souls

Dialogue ◽  
1994 ◽  
Vol 33 (4) ◽  
pp. 701-724 ◽  
Author(s):  
Murray Miles
Keyword(s):  
The Other ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Human Beings ◽  
Mental Processes ◽  
Other Hand ◽  
Forms Of Life ◽  
The One

InLeibniz: Perception, Apperception, and Thought, Robert McRae alleges a flat “contradiction” (McRae 1976, p. 30) at the heart of Leibniz's doctrine of three grades of monads: bare entelechies characterized by perception; animal souls capable both of perception and of sensation; and rational souls, minds or spirits endowed not only with capacities for perception and sensation but also with consciousness of self or what Leibniz calls (introducing a new term of art into the vocabulary of philosophy) “apperception.” Apperception is a necessary condition of those distinctively human mental processes associated with understanding and with reason. Insofar as it is also a sufficient condition of rationality, it is not ascribable to animals. But apperception is a necessary condition of sensation or feeling as well; and animals are capable of sensation, according to Leibniz, who decisively rejected the Cartesian doctrine that beasts are nothing but material automata. “On the one hand,” writes McRae, “what distinguishes animals from lower forms of life is sensation or feeling, but on the other hand apperception is a necessary condition of sensation, and apperception distinguishes human beings from animals” (McRae 1976, p. 30). “We are thus left with an unresolved inconsistency in Leibniz's account of sensation, so far as sensation is attributable both to men and animals” (ibid., p. 34).

scholarly journals Dissipative conformal measures on locally compact spaces

2014 ◽  
Vol 36 (2) ◽  
pp. 649-670 ◽  
Author(s):  
KLAUS THOMSEN
Keyword(s):  
Operator Algebras ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Ruelle Operator ◽  
Conformal Measures ◽  
Continuous Potential ◽  
The One ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

scholarly journals Subharmonic orbits in an anharmonic oscillator

1997 ◽  
Vol 38 (3) ◽  
pp. 307-315 ◽  
Author(s):  
J. R. Christie ◽  
K. Gopalsamy ◽  
M. P. Panizza
Keyword(s):  
Differential Equations ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Dynamical Behaviour ◽  
Sufficient Condition ◽  
One Dimensional ◽  
Perturbed System ◽  
Melnikov Theory ◽  
The One ◽  
Subharmonic Orbits

AbstractIn a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.

The Order Structure of Positive Operators

2006 ◽  
pp. 1-77 ◽  
Author(s):  
Charalambos D. Aliprantis ◽  
Owen Burkinshaw
Keyword(s):  
Positive Operators ◽  
Order Structure
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