In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures Mba(Σ,L(X,Y )). This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures Mba(Σ,L1(X,Y )). This result has interesting applications in optim...

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A BC where B is a continuous map and C is a continuous linear weakly compact operator from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Kra...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

Let X be a real separable Banach space. The boundary value problem x′ ∈ A(t)x + F (t, x), t ∈ R+, Ux = a, (B) is studied on the infinite interval R+ = [0,∞). Here, the closed and densely defined linear operator A(t) : X ⊃ D(A)→ X, t ∈ R+, generates an evolution operator W (t, s). The function F : R+×X → 2X is measurable in its first variable, upper semicontinuous in its second and has weakly co...