Related papers: Disjointness preserving $\mathrm{C}_0$-semigroups …

We study a semigroup $\phi$ of linear operators acting on a Banach space $X$ which satisfies the condition $\codim X_0<\infty$, where $X_0=\{x\in X \mid \phi_t(x)\underset{t\to\infty}\longrightarrow 0\}.$ We show that $X_0$ is closed under…

Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…

We study compactness along orthonormal (disjoint bounded) sequences for operators from Hilbert spaces (Banach lattices) to Frechet spaces.

We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We establish multilinear and polynomial versions of [23, Theorem B]…

We initiate a study of structural properties of the quotient algebra $\mathcal K(X)/\mathcal A(X)$ of the compact-by-approximable operators on Banach spaces $X$ failing the approximation property. Our main results and examples include the…

The semi-local convergence analysis of a well defined and efficient two-step Secant method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed…

Linear maps between finite-dimensional ordered vector spaces with orders induced by proper cones $C_A$ and $C_B$ are called entanglement breaking if their partial application sends the maximal tensor product $K\otimes_{\max} C_A$ into the…

Let $\Omega \subset {\bf R}^d$ be an open bounded set with Lipschitz boundary $\Gamma$. Let $D_V$ be the Dirichlet-to-Neumann operator with respect to a purely second-order symmetric divergence form operator with real Lipschitz continuous…

We study the class of $(p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for…

In this paper we introduce a new decomposition of power-bounded operators, analogous to the Jacobs-deLeeuw-Glicksberg decomposition. This is done using so-called K\"ohler semigroups and the general theory of right topological compact…

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…

For an operator $A$ on a complex Banach space $X$ and a closed subspace $M\subseteq X$, the local commutant of $A$ at $M$ is the set $C(A;M)$ of all operators $T$ on $X$ such that $TAx=ATx$ for every $x\in M$. It is clear that $ C(A;M)$ is…

Using Ostaszewski's $\clubsuit$-principle, we construct a non-metrizable, locally compact, scattered space $L$ in which the operators on the Banach space $C_0(L \times L)$ exhibit a remarkably simple structure. We provide a detailed…

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schr\"odinger type equations.…

Let $X$ be a completely regular space. For a non-vanishing self-adjoint Banach subalgebra $H$ of $C_B(X)$ which has local units we construct the spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of the Stone-Cech compactification of…

Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schr\"odinger operator on the complete graph. The operators exhibits…

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…

Let $({\cal X},\|\:.\:\|)$ be a Banach space. In general, for a $C_0$-semigroup \semi on $({\cal X},\|\:.\:\|)$, its adjoint semigroup \semia is no longer strongly continuous on the dual space $({\cal X}^{*},\|\:.\:\|^{*})$. Consider on…

We consider locally equi-continuous strongly continuous semigroups on locally convex spaces (X,tau). First, we show that if (X,tau) has the property that weak* compact sets of the dual are equi-continuous, then strong continuity of the…

The well-known Batty's theorem states that if a $C_0$-semigroup $T(t)$ is bounded and the spectrum of the generator $A$ is contained in the open left-half plane of $\mathbb{C}$, then $\|T(t)A^{-1}\|$ tends to $0$. This can be thought of as…