Related papers: The operator Fejer-Riesz theorem

Frames and orthonormal bases are naturally linked to bounded operators. To tackle unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also…

We extend the concept of conditional supremum to the measure-free setting of Riesz spaces via the conditional expectation operator. We explore its properties and show how this tool is crucial in generalizing various results across multiple…

In this paper we give necessary and sufficient conditions for a bounded linear operator $T$ to be generalized Drazin-Riesz invertible or generalized Drazin-meromorphic invertible. Also, we study generalized Browder's theorem and generalized…

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…

We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with…

Several spectra of analytically Riesz operators will be characterized. These results will led to prove Weyl and Browder type theorems for the aforementioned class of operators.

Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…

We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial…

The present work deals with the mathematical investigation of some generalizations of the Sz\'{a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz\'{a}sz operators involving multiple…

We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow \mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to $\mathrm{FIN}_{j}$ for…

Rhaly operators, as generalizations of the Ces\`aro operator, are studied from the standpoint of view of spectral theory and invariant subspaces, extending previous results by Rhaly and Leibowitz to a framework where generalized Ces\`aro…

We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…

We revisit the properties of Bessel-Riesz operators and refine the proof of the boundedness of these operators on generalized Morrey spaces using Young's inequality. We also obtain an estimate for the norm of these operators on generalized…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the abstract space with measure was obtained in current paper. Some applications to classical harmonic analysis were reviewed.

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…

We describe the Riesz completion (in the sense of van Haandel) of some spaces of regular operators as explicitly identified subspaces of the regular operators into larger range spaces

We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.

We study generalizations of the classical Bernstein operators on polynomial spaces, where instead of fixing $\mathbf{1}$ and $x$, we require that $\mathbf{1}$ and a strictly increasing polynomial $f_1$ be fixed. Via several examples, we…

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…