• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1185-1192
• /
• 2020

In this paper, we introduce and investigate multi subspace-hypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M-hypercyclic or multi M-hypercyclic, then Tⁿ is multi M-hypercyclic for any natural number n and by using this result, make some examples of multi subspace-hypercyclic operators. We prove that multi M-hypercyclic operators have somewhere dense orbits in M. We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.147-154
• /
• 2009

Tamanoi proposed higher Schwarzian operators which include the classical Schwarzian derivative as the first nontrivial operator. In view of the relations between the classical Schwarzian derivative and the analogous differential operator defined in terms of Peschl's differential operators, we define the generating function of our generalized higher operators in terms of Peschl's differential operators and obtain recursion formulas for them. Our generalized higher operators include the analogous differential operator to the classical Schwarzian derivative. A special case of our generalized higher Schwarzian operators turns out to be the Tamanoi's operators as expected.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.367-378
• /
• 2018

In this paper, we study m-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize m-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols ${\varphi}$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols ${\varphi}$ to be m-expansive or m-contractive. Finally, we give some results for m-expansive and m-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols ${\varphi}$.

• Korean Journal of Mathematics
• /
• v.6 no.1
• /
• pp.1-7
• /
• 1998

We introduce the notions of McShane-Stieltjes representable operators nearly McShane-Stieltjes representable operators and then investigate some properties of theses operators.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.259-275
• /
• 2007

The continuity for the multilinear operators associated to some non-convolution type integral operators on Besov spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.541-564
• /
• 2007

In this paper, the endpoint estimates for some multilinear operators related to certain integral operators are obtained. The operators include Littlewood-Paley operators and Marcinkiewicz operators.

• Korean Journal of Mathematics
• /
• v.13 no.1
• /
• pp.61-82
• /
• 2005

We characterize Gaussian cotype X operators acting between Banach spaces, where X is a Banach sequence space. Further we give an extensive presentation of results on the connections between cotype and summing operators.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.255-273
• /
• 2005

We characterize Gaussian cotype X operators acting between Banach spaces, where X is a Banach sequence space. Further we give an extensive presentation of results on the connections between cotype and summing operators.

• Journal of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1203-1223
• /
• 2011

In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.621-627
• /
• 2012

Star operations are defined by R. E. Hodel in 1994. In this paper some relations among star operators, sequential closure operators and closure operators are discussed. Moreover, we introduce an induced topology by a family of subsets of a space, and some interesting results about star operators are established by the induced topology.