Some properties of subspace convex-cyclic operators

Ahmed, Dilan; Hama, Mudhafar; Woźniak, J.

doi:10.17656/jzs.10797

Cited by 1 publication

(2 citation statements)

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“…The sequence of functions x k : Y → H are defined as x k (y) = 1 λ k y. Also, we define P k (T )y = λ k y. and we use technique Theorem 2.8 in [2] for extending x k to Y by linear functional. This makes sense because the subspace Y is linearly independent.…”

Section: New Subspace Convex-cyclic Operatorsmentioning

confidence: 99%

“…We aim to show that operators with sufficiently many eigenvectors of modulus 1 are subspace convex-cyclic operators. Let us first construct the following definition from Theorems 3.1 and 3.9 in [2] and Theorem 1. Here we have not mentioned any density or properties related to density for details you can see [4], we just join it with collection of eigenvalues and associated eigenvectors of the subspace convex-cyclic orbits that we have named them orbit eigen-spaces.…”

Section: Eigenvalue Measurementioning

confidence: 99%

See 1 more Smart Citation

Central Limit Theorem in View of Subspace Convex-Cyclic Operators

Hasan¹,

Ahmed²,

Hama³

et al. 2021

Bul. Kar. Univ. - Math.

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In our work we have defined an operator called subspace convex-cyclic operator. The property of this newly defined operator relates eigenvalues which have eigenvectors of modulus one with kernels of the operator. We have also illustrated the effect of the subspace convex-cyclic operator when we let it function in linear dynamics and joining it with functional analysis. The work is done on infinite dimensional spaces which may make linear operators have dense orbits. Its property of measure preserving puts together probability space with measurable dynamics and widens the subject to ergodic theory. We have also applied Birkhoff’s Ergodic Theorem to give a modified version of subspace convex-cyclic operator. To work on a separable infinite Hilbert space, it is important to have Gaussian invariant measure from which we use eigenvectors of modulus one to get what we need to have. One of the important results that we have got from this paper is the study of Central Limit Theorem. We have shown that providing Gaussian measure, Central Limit Theorem holds under the certain conditions that are given to the defined operator. In general our work is theoretically new and is combining three basic concepts dynamical system, operator theory and ergodic theory under the measure and statistics theory.

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Section: New Subspace Convex-cyclic Operatorsmentioning

confidence: 99%

Section: Eigenvalue Measurementioning

confidence: 99%