• Communications of the Korean Mathematical Society
• /
• v.8 no.3
• /
• pp.409-413
• /
• 1993

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.873-879
• /
• 1994

• Communications of the Korean Mathematical Society
• /
• v.16 no.2
• /
• pp.235-241
• /
• 2001

In this paper we study some properties of he joint Weyl and Browder spectra for the slightly larger classes containing doubly commuting n-tuples of hyponormal operators.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.533-542
• /
• 2019

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2013-2027
• /
• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.193-226
• /
• 2001

We study Feynman's Operational Calculus for operator-valued functions of time and for measures which are not necessarily probability measures; we also permit the presence of certain unbounded operators. further, we relate the disentangling map defined within the solutions of evolution equations and, finally, remark on the application of stability results to the present paper.

• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.143-159
• /
• 2017

In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.225-251
• /
• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.69-79
• /
• 2020

In this paper, we study the properties of T satisfying [CTC, T] = 0 for some conjugation C where [R, S] := RS - SR. In particular, we show that if T is normal, then [CTC, C] = 0. Moreover, the class of operators T satisfy [CTC, T] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T|C, |T|] = 0.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.53-62
• /
• 2000

In this paper we explore relations between joint Weyl and Browder spectra. Also, we give a spectral characterization of the Taylor-Browder spectrum for special classes of doubly commuting n-tuples of operators and then give a partial answer to Duggal's question.