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The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use…
A classical proof of Pisier's construction of a polynomially bounded operator not similar to a contraction is given.
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
We construct operators which factorize the transfer function associated with a non-self-adjoint 2x2 operator matrix whose diagonal entries can have overlapping spectra and whose off-diagonal entries are unbounded operators.
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.
In this paper, we establish some basic properties of certain operators (element of centroids, averaging operators, derivations, Nijenhuis operators, Rota-Baxter operators) on (compatible) ternary Leibniz algebras and give the classification…
We define an almost periodic extension of the Wiener algebras in the quaternionic setting and prove a Wiener-Levy type theorem for it, as well as extending the theorem to the matrix-valued case. We prove a Wiener-Hopf factorization theorem…
We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…
Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…
In the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power…
In this paper, we present a new algorithm and an experimental implementation for factoring elements in the polynomial n'th Weyl algebra, the polynomial n'th shift algebra, and ZZ^n-graded polynomials in the n'th q-Weyl algebra. The most…
A canonical factorization is given for a quadratic pencil of accretive operators in a Hilbert space. Also, we establish some relationships between an m-accretive operator and its Moore-Penorse inverse. As an application, we study a result…
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras.
Algebraic and analytic aspects of self-adjoint operators of order four or more with polynomial coefficients are investigated. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.