The orbit of a bounded operator under the Möbius group modulo similarity equivalence

Ghara, Soumitra

doi:10.1007/s11856-020-2016-x

Cited by 2 publications

(4 citation statements)

References 4 publications

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“…The next result is a generalization of the result given by S. Ghara in [17] to operator class NFB 2 (D). Proposition 4.7.…”

Section: Again We Obtain Ksupporting

confidence: 67%

“…Clearly, it is a non negative definite kernel. If K 0 , K 1 are two sharp kernels, then so is the matrix-valued kernel function J k (K 0 , K 1 )| res∆ due to S. Ghara in [17]. The following result is also given: Lemma 4.6.…”

Section: Again We Obtain Kmentioning

confidence: 98%

“…The following result is also given: Lemma 4.6. [17] Suppose that K 0 and K 1 are two scalar valued sharp positive definite kernels on D × D. If the multiplication operators M z on (H, K 0 ) and (H, K 1 ) are weakly homogenous, then M z on (H, J k (K 0 , K 1 )| res∆ ) is also weakly homogenous.…”

Section: Again We Obtain Kmentioning

confidence: 99%

“…As its extension, weakly homogeneous operators are defined (see [2,14]). In [17], S. Ghara pointed out the necessary and sufficient conditions for the multiplication by the coordinate function z acting on a Hilbert space H K possessing a sharp reproducing kernel K, to be weakly homogeneous, and gave some nontrivial results on weakly homogeneous, so that many high index weakly homogeneous operators were obtained. So far, the characterization of weakly homogeneous operators remains a challenging problem, even for operators of index one in the Cowen-Douglas class.…”

Section: Introductionmentioning

confidence: 99%

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The irreducibility and strong irreducibility of operators

Jiang¹,

Wang²

2023

Strongly Irreducible Operators on Hilbert Space

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To construct more homogeneous operators, B. Bagchi and G. Misra in [2] introduced the operator T0 T0−T1 0 T1and proved that when T 0 and T 1 are homogeneous operators with the same unitary representation U (g), it is homogeneous with associated representation U (g) ⊕ U (g). At the same time, they asked an open question, is the constructed operator irreducible? A. Korányi in [31] showed that when the (1,2)-entry of the matrix is α(T 0 − T 1 ), α ∈ C the above result is also valid, and their unitary equivalence class depends only on |α|. In this case, he and S. Hazra [20] gave a large class of irreducible homogeneous bilateral 2 × 2 block shifts, respectively, which are mutually unitarily inequivalent for α > 0. In this note, we generalize the construction to T = T0 XT1−T0X 0 T1and provide some sufficient conditions for its irreducibility. We also find that for the above-mentioned T 0 , T 1 and non-scalar operator X, T is weakly homogeneous rather than homogeneous. So the weak homogeneity problem related to T is investigated.

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“…The next result is a generalization of the result given by S. Ghara in [17] to operator class NFB 2 (D). Proposition 4.7.…”

Section: Again We Obtain Ksupporting

confidence: 67%

Section: Again We Obtain Kmentioning

confidence: 98%

Section: Again We Obtain Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations