Related papers: Cowen-Douglas operators and analytic continuation
A covariant approach to the conformal property associated with Moyal-Lax operators is given. By identifying the conformal covariance with the second Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the primary fields of…
We characterize the inverse of an analytic Fredholm operator-valued function A(z) near an isolated singularity within a general Banach space framework. Our approach relies on the sequential factorization of A(z) via Fredholm quotient…
In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is…
In this paper, we endow the space of continuous translation invariant valuation on convex sets generated by mixed volumes coupled with a suitable Radon measure on tuples of convex bodies with two appropriate norms. This enables us to…
Let $A$ be a unital Banach algebra. We give a characterization of the left Banach $A$-modules $X$ for which there exists a commutative unital $C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive unital homomorphism…
In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this way we give a positive answer to a question posed by Bauschke and Wang in [4].
We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced…
We study (almost) limited operators in Banach lattices and their relations to L-weakly compact, semi-compact, and Dunford-Pettis operators. Several further related topics are investigated.
Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces $L_p$ are constructed.
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
A remarkable result by S. Artstein-Avidan and V. Milman states that, up to pre-composition with affine operators, addition of affine functionals, and multiplication by positive scalars, the only fully order preserving mapping acting on the…
Let $T$ be a bounded linear operator on a complex separable infinite dimensional Hilbert space $\mathcal{H}$. $T$ is called intransitive if it leaves invariant spaces other than 0 or the whole space $\mathcal{H}$; otherwise it is…
On a reflexive Banach space $X$, if an operator $T$ admits a functional calculus for the absolutely continuous functions on its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional calculus can always be extended to include all…
We study approximately orthogonality (in the sense of Dragomir) preserving and reversing operators. We show that for some orthogonality notations, an operator defined from a finite-dimensional Banach space to a normed linear space is…
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…
Sequences of $n$-th order bidual Banach spaces, called tower systems and their direct and inverse limits are considered. Motivated by recent applications in uniform algebras, we introduce two functors: $\textrm{Dir}$ and $\textrm{Inv}$…
We introduce the notion of stochastic product as a binary operation on the convex set of quantum states (the density operators) that preserves the convex structure, and we investigate its main consequences. We consider, in particular,…
With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is…
We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This…
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…