Related papers: Characterization of Lie centralizable mappings on …

Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is called polynomial if it is a submodule of the K[X]-module…

Let $X(\mathbb{Z})$ be a reflexive rearrangement-invariant Banach sequence space with nontrivial Boyd indices $\alpha_X,\beta_X$ and let $w$ be a symmetric weight in the intersection of the Muckenhoupt classes $A_{1/\alpha_X}(\mathbb{Z})$…

Let $X$ and $Y$ be Banach spaces, let $\mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $P\colon\mathcal{A}(X)\to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the…

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X with dim X greater than 3. In this paper, we characterize the forms of surjective linear maps on B(X) which preserve the dimension of the vector space…

We present the following reflexivity-like result concerning the automorphism group of the $C^*$-algebra B(H), H being a separable Hilbert space. Let $\phi:B(H)\to B(H)$ be a multiplicative map (no linearity or continuity is assumed) which…

A space $X$ is said to be hereditarily indecomposable if no two (infinite dimensional) subspaces of $X$ are in a direct sum. In this paper, we show that if $X$ is a complex hereditarily indecomposable Banach space, then every operator from…

Let $L$ be a Lie algebra over a field of characteristic different from $2$. If $L$ is perfect and centerless, then every skew-symmetric biderivation $\delta:L\times L\to L$ is of the form $\delta(x,y)=\gamma([x,y])$ for all $x,y\in L$,…

Let $\mathcal A$ be a Banach algebra for which the group of invertible elements is connected. A subspace $\mathcal L \subseteq \mathcal A$ is a Lie ideal in $\mathcal A$ if, and only if, it is invariant under inner automorphisms. This…

Given a complex Banach space $X$, let $\mathcal{B}(X)$ be the collection of all bounded linear operators on $X.$ For $A,B\in\mathcal{B}(X)$ we define $A,B$ are $A$-weakly commutative if there exists $C\in\mathcal{B}(X)$ satisfying…

Let $A$ be a unital Banach $\star$-algebra with unity $1$, $X$ be a Banach space and $\phi : A \times A \to X$ be a continuous bilinear map. We characterize the structure of $\phi$ where it satisfies any of the following properties: $$a,b…

Let ${\mathcal N}$ and ${\mathcal M}$ be nests on Banach spaces $X$ and $Y$ over the (real or complex) field $\mathbb F$ and let $\mbox{\rm Alg}{\mathcal N}$ and $\mbox{\rm Alg}{\mathcal M}$ be the associated nest algebras, respectively. It…

We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element…

Given $X$ a complex Banach space, $L$ a complex nilpotent finite dimensional Lie algebra, and $\rho\colon L\to L(X)$, a representation of $L$ in $X$ such that $\rho (l)\in K(X)$ for all $l\in L$, the Taylor, the Slodkowski, the Fredholm,…

Let M be a real analytic manifold modeled on a locally convex space and K be a non-empty compact subset of M. We show that if an open neighborhood of K in M admits a complexification which is a regular topological space, then the germ of…

Let $A$ be a Banach algebra with a bounded left approximate identity $\{e_\lambda\}_{\lambda\in\Lambda}$, let $\pi$ be a continuous representation of $A$ on a Banach space $X$, and let $S$ be a non-empty subset of $X$ such that…

Let G be an amenable group, let X be a Banach space and let \pi : G --> B(X) be a bounded representation. We show that if the set {\pi(t) : t \in G} is gamma-bounded then \pi extends to a bounded homomorphism w : C*(G) --> B(X) on the group…

Let $\mathcal{B} (X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$. For an operator $ T \in \mathcal{B} (X)$, $K(T)$ denotes as usual the analytic core of $T$. We determine the form of…

Let $A$ be a Banach algebra admitting a bounded approximate unit and satisfying property $\mathbb{B}$. Suppose $T: A \rightarrow X$ is a continuous linear map, where $X$ is an essential Banach $A$-bimodule. We prove that the following…

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps $T:A\to B$ between Banach…

Suppose $X$ is a compact Hausdorff space. In terms of topolocical properties of $X$, we find topological conditions on $X$ that are equivalent to each of the following: 1. every additive local multiplication on $C\left( X\right) $ is a…