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On Connection between Characterestic Functions and the Caratheodori Class Functions

Zolotarev, Vladimir A., Hatamleh, Raéd (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47A65, 45S78.Connection of characteristic functions S(z) of nonunitary operator T with the functions of Caratheodori class is established. It was demonstrated that the representing measures from integral representation of the function of Caratheodori's class are defined by restrictions of spectral measures of unitary dilation, of a restricted operator T on the corresponding defect subspaces.

On operators with unitary ϱ-dilations

T. Ando, K. Takahashi (1997)

Annales Polonici Mathematici

We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class C ϱ , then T itself is unitary.

On the canonical development of Parseval formulas for singular differential operators

Robert W. Carroll (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per funzioni opportune f , g si ottiene una formula di Parseval ⟨ 𝐑 Q , 𝒬 ⁢ f ⁢ 𝒬 ⁢ g ⟩ λ = ⟨ Δ Q - 1 / 2 ⁢ f , Δ Q - 1 / 2 ⁢ g ⟩ per operatori differenziali singolari di tipo dell'operatore radiale di Laplace-Beltrami. 𝐑 Q è una funzione spettrale generalizzata di tipo Marčenko e può essere rappresentata per mezzo di un certo nucleo della trasmutazione.

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger (1997)

Annales Polonici Mathematici

Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if f ( σ W ( T ) ) ∪ z ∈ ℂ : | z | = 1 is connected, where σ W ( T ) denotes the Weyl spectrum of T.

Operators on a Hilbert space similar to a part of the backward shift of multiplicity one

Yoichi Uetake (2001)

Studia Mathematica

Let A: X → X be a bounded operator on a separable complex Hilbert space X with an inner product ⟨ · , · ⟩ X . For b, c ∈ X, a weak resolvent of A is the complex function of the form ⟨ ( I - z A ) - 1 b , c ⟩ X . We will discuss an equivalent condition, in terms of weak resolvents, for A to be similar to a restriction of the backward shift of multiplicity 1.

Order bounded orthosymmetric bilinear operator

Elmiloud Chil (2011)

Czechoslovak Mathematical Journal

It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b : E × E → F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f -algebras.

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