Hyperexpansive composition operators

ZENON J. JABŁOŃSKI

doi:10.1017/S0305004103006844

Abstract

The notion of a completely hyperexpansive operator has been introduced in [2] by Athavale. In this paper bounded and unbounded hyperexpansive composition operators are investigated. A unique semispectral measure is associated with a bounded completely hyperexpansive composition operator. Examples of bounded and unbounded densely defined $2$-isometric (completely hyperexpansive, $2$-hyperexpansive) composition operators with invariant domains are given.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Jabłoński, Z. J. 2008. A moment theorem for completely hyperexpansive operators. Acta Mathematica Hungarica, Vol. 120, Issue. 1-2, p. 21.

Jabłoński, Zenon J. Jung, Il Bong Kwak, Jung Ah and Stochel, Jan 2011. Hyperexpansive completion problem via alternating sequences; an application to subnormality. Linear Algebra and its Applications, Vol. 434, Issue. 12, p. 2497.

Budzyński, Piotr 2012. A Note on Unbounded Hyponormal Composition Operators inL2-Spaces. Journal of Function Spaces and Applications, Vol. 2012, Issue. , p. 1.

Budzyński, Piotr Jabłoński, Zenon Jan Jung, Il Bong and Stochel, Jan 2014. A multiplicative property characterizes quasinormal composition operators in L2-spaces. Journal of Mathematical Analysis and Applications, Vol. 409, Issue. 1, p. 576.

Budzyński, Piotr Jabłoński, Zenon Jan Jung, Il Bong and Stochel, Jan 2014. On unbounded composition operators in $$L^2$$ -spaces. Annali di Matematica Pura ed Applicata, Vol. 193, Issue. 3, p. 663.

Gu, Caixing 2015. Functional calculus for m-isometries and related operators on Hilbert spaces and Banach spaces. Acta Scientiarum Mathematicarum, Vol. 81, Issue. 3-4, p. 605.

Budzyński, Piotr Jabłoński, Zenon Jan Jung, Il Bong and Stochel, Jan 2015. Unbounded subnormal composition operators in L2-spaces. Journal of Functional Analysis, Vol. 269, Issue. 7, p. 2110.

Chavan, Sameer and Trivedi, Shailesh 2016. An analytic model for left-invertible weighted shifts on directed trees: Table 1.. Journal of the London Mathematical Society, Vol. 94, Issue. 1, p. 253.

KARIMI, Lotfollah FAGHIH-AHMADI, Masoumeh and HEDAYATAN, Karim 2016. Some properties of concave operators. TURKISH JOURNAL OF MATHEMATICS, Vol. 40, Issue. , p. 1211.

Budzyński, Piotr Jabłoński, Zenon Jan Jung, Il Bong and Stochel, Jan 2016. A subnormal weighted shift on a directed tree whose nth power has trivial domain. Journal of Mathematical Analysis and Applications, Vol. 435, Issue. 1, p. 302.

Chavan, Sameer Pradhan, Deepak Kumar and Trivedi, Shailesh 2017. Dirichlet Spaces Associated with Locally Finite Rooted Directed Trees. Integral Equations and Operator Theory, Vol. 89, Issue. 2, p. 209.

Budzyński, Piotr Dymek, Piotr and Płaneta, Artur 2017. Quasinormal extensions of subnormal operator-weighted composition operators in ℓ2-spaces. Journal of Mathematical Analysis and Applications, Vol. 452, Issue. 1, p. 27.

Estaremi, Y. and Shamsigamchi, S. 2017. Unbounded Hyperexpansive Weighted Composition Operators on $$L^{2} (\varSigma )$$ L 2 ( Σ ) . Iranian Journal of Science and Technology, Transactions A: Science, Vol. 41, Issue. 3, p. 671.

Budzyński, Piotr Jabłoński, Zenon Jan Jung, Il Bong and Stochel, Jan 2017. Subnormality of unbounded composition operators over one-circuit directed graphs: Exotic examples. Advances in Mathematics, Vol. 310, Issue. , p. 484.

Anand, Akash Chavan, Sameer Jabłoński, Zenon Jan and Stochel, Jan 2019. A solution to the Cauchy dual subnormality problem for 2-isometries. Journal of Functional Analysis, Vol. 277, Issue. 12, p. 108292.

Anand, Akash Chavan, Sameer Jabłoński, Zenon Jan and Stochel, Jan 2020. The Cauchy dual subnormality problem for cyclic 2-isometries. Advances in Operator Theory, Vol. 5, Issue. 3, p. 1061.

Jabłoński, Zenon Jan and Kośmider, Jakub 2021. $$\varvec{m}$$–Isometric Composition Operators on Directed Graphs with One Circuit. Integral Equations and Operator Theory, Vol. 93, Issue. 5,

Kośmider, Jakub 2021. The Wold-Type Decomposition for m-Isometries. Bulletin of the Malaysian Mathematical Sciences Society, Vol. 44, Issue. 6, p. 4155.

Lata, Sneh Pokhriyal, Sushant and Singh, Dinesh 2022. Multivariable sub-Hardy Hilbert spaces invariant under the action of n-tuple of finite Blaschke factors. Journal of Mathematical Analysis and Applications, Vol. 512, Issue. 2, p. 126184.

Saddi, Adel and Mahmoudi, Fatma 2023. n-Quasi-m-contractive and n-quasi-m-expansive operators on a Hilbert space. Asian-European Journal of Mathematics, Vol. 16, Issue. 08,

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Hyperexpansive composition operators

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