Related papers: Lip-Linear operators and their connection to Lipsc…

We consider bisingular pseudodifferential operators which are pseudodifferential operators of tensor product type. These operators are defined on the product manifold $M_1 \times M_2$, for closed manifolds $M_1$ and $M_2$. We prove a…

We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…

Real linear operators between two complex Banach spaces unify naturally two important classes of linear operators and antilinear operators. We give a survey of basic geometric, spectral and duality properties of real linear operators. The…

Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of…

We investigate dynamical properties of linear operators that are obtained as the linearization of Lipschitz self-maps defined on a pointed metric space. These operators are known as Lipschitz operators. More concretely, for a Lipschitz…

We construct a family of bilinear differential operators which satisfy certain gauge properties. These operators can be naturally associated with $q$-deformations of classical integrable hierarchies. In particular, we consider the case when…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a…

Let $\mathfrak{g}$ be a vector space and $[,],[,]'$ be a pair of Lie brackets on $\mathfrak{g}$. By definition they are compatible if $[,]+[,]'$ is again a Lie bracket. Such pairs play important role in bihamiltonian and $r$-matrix…

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…

We study the existence of continuous (linear) operators from the Banach spaces $\mbox{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces $M$ vanishing at a distinguished point and from their predual spaces $\mathcal{F}(M)$ onto…

We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam…

Let $X_1, \ldots, X_m$ be Banach spaces and let $E_1, \ldots, E_m,F$ be Banach lattices. Our main results read as follows: (i) The linear adjoint $A^*$ of a continuous multilinear operator $A \colon X_1 \times \cdots \times X_m \to F$ is…

Let D be the ring of differential operators on a smooth irreducible affine variety X over the complex numbers; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded…

The purpose of this paper is to obtain an integral representation for the difference $f(L_1)-f(L_2)$ of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish…

Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where…

It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also…

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…

Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…

We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…