‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

In this paper, we characterize a class of additive maps on Hilbert C∗-modules which maps a ”rank one” adjointable operators to another rank one operators.

In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C∗-algebra and the relationship between the set of all adjointable operators from a Hilbert A -module E to a Hilbert A module F and the set of all adjointable operators from the multiplier module M(E) of E to the multiplier module M(F ) of F.

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

Let $$\mathcal {H}$$ be a Hilbert space, A positive definite operator in and $$\langle f,g\rangle _A=\langle Af,g\rangle $$ , $$f,g\in \mathcal the A-inner product. This paper studies geometry of set $$\begin{aligned} {I}_A^a:=\{\text { adjointable isometries for } \langle \ \rangle _A\}. \end{aligned}$$ It is proved that {I}_A^a$$ submanifold Banach algebra operators, homogeneous space group i...

It is well known that a function K : Ω × Ω → L(Y) (where L(Y) is the set of all bounded linear operators on a Hilbert space Y) being (1) a positive kernel in the sense of Aronszajn (i.e. ∑N i,j=1〈K(ωi, ωj)yj , yi〉 ≥ 0 for all ω1, . . . , ωN ∈ Ω, y1, . . . , yN ∈ Y, and N = 1, 2, . . . ) is equivalent to (2) K being the reproducing kernel for a reproducing kernel Hilbert space H(K), and (3) K ha...

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...