• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.217-227
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• 2024

Let G be an infinite countable group and A be a finite set. If Σ ⊆ A^G is a strongly irreducible subshift of finite type and 𝓖 is the local conjugacy equivalence relation on Σ. We construct a decreasing sequence 𝓡 of unital C^*-subalgebras of C(Σ) and a sequence of faithful conditional expectations E defined on C(Σ), and obtain a Toeplitz algebra 𝓣 (𝓡, 𝓔) and a C^*-algebra C^*(𝓡, 𝓔) for the pair (𝓡, 𝓔). We show that C^*(𝓡, 𝓔) is *-isomorphic to the reduced groupoid C^*-algebra C^*_r(𝓖).

• Journal of the Korean Mathematical Society
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• v.31 no.2
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• pp.289-307
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• 1994

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.507-513
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• 2018

We will consider the asymptotic toeplitzness associated with weighted composition operators on the Hardy-Hilbert space $H^2$.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.377-385
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• 2009

Twenty five female students in Seoul participated and were divided into two group in the experiment of weight loss effect of two treatments. Fourteen students(Treatment A group), randomly chosen from the students, had fed on diet foods and exercised over 8 weeks, and the remaining students(Treatment B group) had fed on diet foods only for the same periods. Weights of 25 students had been measured repeatedly four times at an interval of two weeks during 8 weeks, It resulted from mixed model analysis of repeated measurements data that separate Toeplitz pattern for each treatment group was selected as the optimal covariance pattern. Based upon the optimal covariance pattern model, the baseline effect and time effect were found to be highly significant, but the treatment-time interaction effect was found to be insignificant. Finally, the students with diet foods and exercises were more effective in losing weight than the students with only diet foods were.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.149-156
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• 1991

The theory of the asymptotic behavior of Toeplitz forms is applicable to some problems concerning the local limit theorem.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.1-9
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• 1997

We obtained some class fields associated to an order R of a function field and evaluated the valuation of the invariant $\xi (c)$ for an invertible ideal c of R.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.901-906
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• 2014

In this note we provide a concrete description on the invariant subspaces for the backward shift on the Hardy space $H^2(\mathbb{T})$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1471-1481
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• 2016

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.