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JournalISSN: 1385-1292

Positivity 

Springer Science+Business Media
About: Positivity is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Operator theory & Banach space. It has an ISSN identifier of 1385-1292. Over the lifetime, 1416 publications have been published receiving 11472 citations. The journal is also known as: An international journal devoted to the theory and applications of positivity in analysis.


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Journal ArticleDOI
TL;DR: In this article, a short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered.
Abstract: We provide an introduction to the theory of interior-point algorithms of optimization based on the theory of Euclidean Jordan algebras. A short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered. Connections with the Linear monotone complementarity problem are discussed. Complexity estimates in terms of the rank of the corresponding Jordan algebra are obtained. Necessary results from the theory of Euclidean Jordan algebras are presented.

218 citations

Journal ArticleDOI
TL;DR: In this article, the conservativeness of a Feller semigroup is analyzed in terms of the symbol T T and the necessary and sufficient conditions for the conservativity of the semigroup which are expressed through the symbol.
Abstract: Let $$\{ T_t \} _{t \geqslant 0} $$ denote a Feller semigroup on $$C_\infty (\mathbb{R}^n )$$ , and $$\{ \tilde T_t \} _{t \geqslant 0} $$ itsextension to the bounded measurable functions. We show that $$T_t 1 \in C_b (\mathbb{R}^n )$$ . If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.

115 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if B has finite Szlenk index (for all e > 0) then B can be renormed to have the weak* uniform Kadec-Klee property.
Abstract: Let B be a separable Banach space and let X=B * be separable. We prove that if B has finite Szlenk index (for all e > 0) then B can be renormed to have the weak* uniform Kadec-Klee property. Thus if e > 0 there exists δ (e) > 0 so that if x n is a sequence in the ball of X converging ω* to x so that $$\lim \inf _{n \to \infty } \left\| {x_n - x} \right\| \geqslant \varepsilon {\text{ then }}\left\| x \right\| \leqslant 1 - \delta (\varepsilon )$$ . In addition we show that the norm can be chosen so that δ (e) ≥ cep for some p 0.

114 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied diffusion problems associated with nonlinear diffusions of nonlocal type and gave existence and uniqueness results for these kind of problems and investigated the asymptotic behaviour.
Abstract: The goal of this paper is to study diffusion problems associated with nonlinear diffusions of nonlocal type. We give existence and uniqueness results for these kind of problems and investigate the asymptotic behaviour.

108 citations

Journal ArticleDOI
Abstract: Given monotone operators on the positive orthant in n-dimensional Euclidean space, we explore the relation between inequalities involving those operators, and induced monotone dynamical systems. Attractivity of the origin implies stability for these systems, as well as a certain inequality, the no-joint-increase condition. Under the right perspective the converse is also true. In addition we construct an unbounded path in the set where trajectories of the dynamical system decay monotonically, i.e., we solve a positive continuous selection problem.

99 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202332
2022121
2021116
202081
201976
201893