Related papers: Descriptive set theoretic methods applied to stric…

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable…

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the…

Let $E$ be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra $\mathscr{B}(E)$ of bounded operators on $E$ admits a discontinuous derivation. We show that $\mathscr{B}(E)$ has a singular,…

We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve…

The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

We prove that any normalized block sequence in a Schreier space $X_\xi$, of arbitrary order $\xi<\omega_1$, admits a subsequence equivalent to a subsequence of the canonical basis of some Schreier space. The analogous result is proved for…

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 $T$.

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

Let $\omega_1$ be the first uncountable ordinal. By a result of Rudin, bounded operators on the Banach space $C([0,\omega_1])$ have a natural representation as $[0,\omega_1]\times 0,\omega_1]$-matrices. Loy and Willis observed that the set…

We introduce and study a new class of operators that we call disjoint weak Banach-Saks operators. We establish some characterizations of this class of operators by different types of convergence (norm convergence, unbounded order…

In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this…

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 paper we study singular integral operators which are hyper or weak over Lipschitz or Holder spaces and over weghted Sobolev spaces defined on unbounded domains in the standard $n$-D space $R^n$ for $n>0$. The $\pi$-operator in this…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

Let S be a dense sub-semigroup of the positive real numbers, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a…

We consider complex resonances for discrete and continuous Schr\"odinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in the continuum limit. The potential is supposed to be a sum…

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete…

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…

We show that operators on a separable infinite dimensional Banach space $X$ of the form $I +S$, where $S$ is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on $X$, in fact in the closure…