Roots of operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Roots of Toeplitz Operators on the Bergman Space

One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane C is a complete description of the commutant of a given Toeplitz operator, that is the set of all Toeplitz operators that commute with it. In [4], the first author obtained a complete description of the commutant of Toeplitz operator T with any quasihomogeneous symbol φ(...

On Roots of Eigenpolynomials for Degenerate Exactly-Solvable Differential Operators

In this paper we partially settle our conjecture from [1] on the roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator we establish a lower bound (which supports our conjecture) for the largest modulus of all roots of its unique and monic eigenpolynomial pn as the degree n tends to infinity. The main theorem below thus extends earlier results obtaine...

On Quantized Algebra of Wess-zumino Differential Operators at Roots of Unity

Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System

In this paper, we introduce a new differential-difference operator Tξ (ξ ∈ R ) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this o...