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An analogue of Kakutani's representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of $C(K)$ precisely as those with a positive approximate identity…

For locally convex spaces $X$ and $Y$, the continuous linear map $T:X \to Y$ is said to be bounded if it maps zero neighborhoods of $X$ into bounded sets of $Y$. We denote $(X,Y) \in \mathcal{B}$ when every operator between $X$ and $Y$ is…

Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where…

Associated to a nonzero homomorphism $\varphi$ of a Banach algebra $A$, we regard special functionals, say $m_\varphi$, on certain subspaces of $A^\ast$ which provide equivalent statements to the existence of a bounded right approximate…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

Let $\mathcal{A}$ and $\mathcal{B}$ be two algebras, let $\mathcal{M}$ be a $\mathcal{B}$-bimodule and let $n$ be a positive integer. A linear mapping $D_n:\mathcal{A} \rightarrow \mathcal{M}$ is called a strongly generalized derivation of…

Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator$.$ The first part of the paper is a survey on applications of such a technique, including a characterization of similarity…

We continue our study of nonperturbative superpotentials of four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, broken to N=1 due to a classical superpotential. In a previous paper, hep-th/0304061, we…

Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\ell^1-$direct sum $A\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\cdot b_2+b_1\cdot a_2+b_1b_2),~~ (a_1, a_2\in A,…

In this paper we consider PI-algebras $A$ over $\R$ or $\C$. It is well known that in general such algebras are not normed algebras. In fact, there is a nilpontent commutative algebra which is not a normed algebra, see [1]. Here we address…

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…

In [8] probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, have been used to show that for every infinite compact spaces K and L there exists a sequence $(\mu_n)$ of…

We continue our investigation, from \cite{dh}, of the ring-theoretic infiniteness properties of ultrapowers of Banach algebras, studying in this paper the notion of being purely infinite. It is well known that a $C^*$-algebra is purely…

We initiate the study of $\lambda$-fold near-factorizations of groups with $\lambda > 1$. While $\lambda$-fold near-factorizations of groups with $\lambda = 1$ have been studied in numerous papers, this is the first detailed treatment for…

Let G be an amenable group, let X be a Banach space and let \pi : G --> B(X) be a bounded representation. We show that if the set {\pi(t) : t \in G} is gamma-bounded then \pi extends to a bounded homomorphism w : C*(G) --> B(X) on the group…

Let $\mathbb{Y}$ be either an Orlicz sequence space or a Marcinkiewicz sequence space. We take advantage of the recent advances in the theory of factorization of the identity carried on in [R. Lechner, Subsymmetric weak* Schauder bases and…

In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras,…

We continue developing the theory around the twin-width of totally ordered binary structures, initiated in the previous paper of the series. We first introduce the notion of parity and linear minors of a matrix, which consists of…

Let $A$ be the $n$-th Weyl algebra over a field of characteristic zero, and $\varphi:A\rightarrow A$ an endomorphism with $S = \varphi(A)$. We prove that if $A$ is finitely generated as a left or right $S$-module, then $S = A$. The proof…

In this paper we present some factorization properties for unbounded local positive maps. We show that an unbounded local positive map $\phi $ on the minimal tensor product of the locally $C^{\ast }$-algebras $\mathcal{A}$ and $C^{\ast…