Search results for " operators"

Solution of an initial-value problem for parabolic equations via monotone operator methods

2014

We study a general initial-value problem for parabolic equations in Banach spaces, by using a monotone operator method. We provide sufficient conditions for the existence of solution to such problem.

MR2986428 Lebedev, Leonid P.(CL-UNC); Vorovich, Iosif I.; Cloud, Michael J. Functional analysis in mechanics. Second edition. Springer Monographs in …

2014

Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property

AbstractLet X be a Banach space. For describing the space P(C[0,1],X) of absolutely summing operators from C[0,1] to X in terms of the space X itself, we construct a tree space ℓ1tree(X) on X. It consists of special trees in X which we call two-trunk trees. We prove that P(C[0,1],X) is isometrically isomorphic to ℓ1tree(X). As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X∗-valued sequence spaces.

On the Bishop-Phelps-Bollobás type theorems

2017

This dissertation is devoted to the study of the Bishop-Phelps-Bollobás property in different contexts. In Chapter 1 we give a historical resume and the motivation behind this property as the classics Bishop-Phelps and Bishop-Phelps-Bollobás theorems. We define the Bishop-Phelps-Bollobás property (BPBp) and we comment on some important current results. In Chapter 2 we study similar properties to the BPBp. First, we define the Bishop-Phelps-Bollobás point property (BPBpp). The BPBpp is stronger than the BPBp. We study it for bounded linear operators and then for bilinear mappings. After that, we study two more similar properties: properties 1 and 2. Property 2 is just the dual property of th…

Existence results and asymptotic behavior for nonlocal abstract Cauchy problems

2008

AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.

Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

2013

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

(H, ρ)-induced dynamics and the quantum game of life

2017

Abstract We propose an extended version of quantum dynamics for a certain system S , whose evolution is ruled by a Hamiltonian H, its initial conditions, and a suitable set ρ of rules, acting repeatedly on S . The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of H, ρ as well as on the initial conditions. After a general discussion on this (H, ρ)-induced dynamics, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.

Some approximation properties by a class of bivariate operators

2019

WOS: 000503431300041

Weak commutation relations of unbounded operators and applications

2011

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.

Variational differential inclusions without ellipticity condition

2020

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.