Related papers: Almost invariant half-spaces of algebras of operat…

We consider the closed subspace of $\ell_\infty$ generated by $c_0$ and the characteristic functions of elements of an uncountable, almost disjoint family $\mathcal A$ of infinite subsets of $\mathbb N$. This Banach space has the form…

For a Banach algebra $A$, we say that an element $M$ in $A\otimes^\gamma A$ is a hyper-commutator if $(a\otimes 1)M=M(1\otimes a)$ for every $a\in A$. A diagonal for a Banach algebra is a hyper-commutator which its image under diagonal…

We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…

Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.

In this article, we completely classify invariant subspaces of finite-rank perturbations of a class of Toeplitz operators on vector-valued Hardy spaces. As a consequence, in the vector-valued setting, we characterize invariant and almost…

We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…

In this article, we first prove the existence of an invariant subspace for a norm-attaining $\ast$-paranormal operator. Then give a representation for $\ast$-paranormal operators in the closure of absolutely norm-attaining operators and…

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1…

We exhibit a Banach space $Z$ failing the approximation property, for which there is an uncountable family $\mathscr F$ of closed subideals contained in the Banach algebra $\mathcal K(Z)$ of the compact operators on $Z$, such that the…

Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups…

We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator is bounded.

We consider the shift operator $M_z$, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. The index of a closed invariant subspace $E$ is defined as $\text{ind}(E) =…

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

We prove that every lattice homomorphism acting on a Banach space $\mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal,…

Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces $A$ of maps from an arbitraty set to a sequence space, that, for every $0 \neq f \in A$, the subset of $A$ of…