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We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the…
In this note, we will define the formulas of curvature and it's covariant derivatives for holomorphic curves on C*-algebras for the multivariable case. As applications, the unitarily and similarly classification theorems for holomorphic…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…
Given a polyanalytic function, we show that the corresponding Toeplitz operator on the Bergman space of the unit disc can be expressed as a quotient of certain differential operators with holomorphic coefficients. This enables us to obtain…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-wise eigenvalues, instead of scalar eigenvalues as in the…
Recently, Cohen and Wales built a faithful linear representation of the Artin group of type $D_n$, hence showing the linearity of this group. It was later discovered that this representation is reducible for some complex values of its two…
This paper makes a modest contribution to the family of starlike univalent mappings in the open unit disk, by the introduction of some new subclasses of them via certain convolution operators. A new univalence condition is given with…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This…
For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the…
The unitary equivalence of $2$-isometric operators satisfying the so-called kernel condition is characterized. It relies on a model for such operators built on operator valued unilateral weighted shifts and on a characterization of the…
The notion of spectral localizer is extended to pairings with semifinite spectral triples. By a spectral flow argument, any semifinite index pairing is shown to be equal to the signature of the spectral localizer. As an application, a…
The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of…
We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued…
In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…
Using the Witten deformation and localization algebra techniques, we compute the $G$-equivariant $K$-homology class of the de Rham operator on a proper cocompact $G$-spin manifold, where $G$ is an almost connected Lie group. By applying a…
Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the…
We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such an SLOCC equivalency class of states is…