Some Isometric Composition Operators

International Journal of Mathematics and Mathematical Sciences, 1979

A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterised.

Complex Analysis and Operator Theory, 2014

In this paper, we study the product of a composition operator Cϕ with the adjoint of a composition operator C * ψ on the Hardy space H 2 (D). The order of the product gives rise to two different cases. We completely characterize when the operator CϕC * ψ is invertible, isometric, and unitary and when the operator C * ψ Cϕ is isometric and unitary. If one of the inducing maps ϕ or ψ is univalent, we completely characterize when C * ψ Cϕ is invertible.

2011

In this paper we characterize the boundedness and invertibility of composition operators on the space m(ϕ, p).

2006

For analytic self-maps ' of the unit disk, we develop a nec- essary and sucient condition for the composition operator C' to be closed-range on the classical Bergman space A 2 . This condition is rela- tively easy to apply. Particular attention is given to the case that ' is an inner function. Included are observations concerning angular deriv- atives

2015

Let Bp,α for p > 1 and α > −1 be the Besov type space of holomorphic functions on the unit disk D. Given φ, a holomorphic self map of D, we show the composition operator Cφ is an isometry on Bp,α if and only if the weighted composition operator Wφ′,φ, is an isometry on the weighted Bergman space Aα. We then characterize isometries among composition operators in Bp,α in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,α, except on B2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces.

m-hikari.com

In this paper, we will be concerned with various results based on generalised Aluthge transformation C r = |C| r U |C| 1−r for 0 < r ≤ 1 and C s,t = |C| s U |C| t for s > 0 and t > 0 of the composition operator C.

Journal of the Australian Mathematical Society, 1992

Let T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.

Complex Analysis and Operator Theory, 2020

We study various properties of composition operators acting between generalized Fock spaces F p ϕ and F q ϕ with weight functions ϕ grow faster than the classical Gaussian weight function 1 2 |z| 2 and satisfy some mild smoothness conditions. We have shown that if p = q, then the composition operator C ψ : F p ϕ → F q ϕ is bounded if and only if it is compact. This result shows a significance difference with the analogous result for the case when C ψ acts between the classical Fock spaces or generalized Fock spaces where the weight functions grow slower than the Gaussian weight function. We further described the Schatten S p (F 2 ϕ) class, normal, unitary, cyclic and supercyclic composition operators. As an application, we characterized the compact differences, the isolated and essentially isolated points, and connected components of the space of the operators under the operator norm topology.

Mathematical Sciences, 2012

In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works. Keywords Common fixed point Á S-metric space Á Compatible mappings Mathematics Subject Classification 47H10 Á 54H25 Sðx; y; zÞ ¼ d 1 ðx; zÞ þ d 2 ðy; zÞ; is an S-metric on X.

In this paper, class A composition operators on L 2 -spaces are characterized and their various properties are studied.

2010

There are many characterizations of isometric operators between Banach spaces. In this paper we give a new characterization of isometries through proximinal sets and remotal sets.

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie a Matematicas, 2006

This paper is a short survey on the numerical range of some composition operators. The first part is devoted to composition operators on the Hilbert Hardy space H 2 on the unit disk. The results are due to P. Bourdon, J. Shapiro and V. Matache. In the second part we study the numerical range of composition operators on the Hilbert space H 2 of Dirichlet series. These results are due to H. Queffélec and the author. The third part is devoted to compactness connected with fixed points in the setting of H 2 and H 2. These results are due to H. Queffélec and the author. Rango numérico de ciertos operadores de composición Resumen. Este trabajo describe un breve panorama sobre el rango numérico de algunos operadores de composición. La primera parte está dedicada a los operadores de composición sobre el espacio de Hilbert Hardy H 2 sobre el disco unidad. Los resultados se deben a P. Bourdon, J. Shapiro y V. Matache. En la segunda parte estudiamos el rango numérico de operadores de composición sobre el espacio de Hilbert H 2 de las series de Dirichlet. Estos resultados se deben a H. Queffélec y a la autora. La tercera parte se dedica a la compacidad relacionada con puntos fijos en el contexto de H 2 y H 2. Estos resultados se deben a H. Queffélec y a la autora.

Archiv der Mathematik, 2008

In this paper we study the point spectrum of the operator

2015

In this paper,we define generalized hyperbolic function classes, we study the composition operator �� from Bloch-type �� spaces to ��,� spaces and from �� ∗ spaces to ��,� spaces. The criteria for these operator to be bounded or compact and Lipschitz continuous are given. Our study also includes the corresponding hyperbolic spaces.

Proceedings of the American Mathematical Society, 2005

We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a σ-finite measure space, Lorentz function spaces on a σ-finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.