Scaled-free objects II

This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps completely bounded on a generation set to a completely bounded linear map of the matrix-normed space. Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods.Comment: 46 pages. Version 4 fixed a few minor typos. Version 3 added matricial completion; fixed an arithmetic error in Example 3.5.10. Version 2 added a preliminaries section on weighted sets and matricial Banach spaces, incorporating much of "Matricial Banach spaces" in summary; fixed a domain issue in Lemma 3.3.2; simplified Examples 3.5.10 and 4.11; added more proofs to Sections 4 and

Ruelle Operator Theorem for Nonexpansive systems

The Ruelle operator theorem has been studied extensively both in dynamical systems and iterated function systems. In this paper we study the Ruelle operator theorem for nonexpansive systems. Our theorems give some sufficient conditions for the Ruelle operator theorem to be held for a nonexpansive system

Characterizations of Ordered Self-adjoint Operator Spaces

In this paper, we generalize the work of Werner and others to develop two abstract characterizations for self-adjoint operator spaces. The corresponding abstract objects can be represented as self-adjoint subspaces of $B(H)$ in such a way that both a metric structure and an order structure are preserved at each matrix level. We demonstrate a generalization of the Arveson Extension Theorem in this context. We also show that quotients of self-adjoint operator spaces can be endowed with a compatible operator space structure and characterize the kernels of completely positive completely bounded maps on self-adjoint operator spaces.Comment: 20 pages. Updated references and corrected typos. The statement of Corollary 3.17 has been strengthene

Operator space characterizations of C*-algebras and ternary rings

We prove that an operator space is completely isometric to a ternary ring of operators if and only if the open unit balls of all of its matrix spaces are bounded symmetric domains. From this we obtain an operator space characterization of C*-algebras.Comment: 20 pages, latex, submitted in November 200

Jensen's Operator Inequality

We establish what we consider to be the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval. This is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions used in earlier versions of the theory. As a consequence, we no longer need to impose conditions on the interval of definition. We show how this relates to the pinching inequality of Davis, and how Jensen's trace inequlity generalizes to C*-algebras..Comment: 12 p

Contractive maps in locally transitive relational metric spaces

Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal., Volume 2013, Article ID 259768] are also being discussed.Comment: arXiv admin note: text overlap with arXiv:1211.417