Approximate point spectra of mm-complex symmetric operators and others (Research on structure of operators by order and related topics)

Let C be a conjugation on a complex Hilbert space H. If {xn} is a sequence of unit vectors, then so is {Cxn}- Under the assumption such that (T - λ)xn → 0 (n → ∞), we show spectral properties concerning with a sequence {Cxn} of unit vectors

Polaroid type operators under quasi-affinities

AbstractIn this paper we study the preservation of some polaroid conditions under quasi-affinities. As a consequence, we derive several results concerning the preservation of Weyl type theorems and generalized Weyl type theorems under quasi-affinities

Remarks on conjugation and antilinear operators and their numerical range (Research on structure of operators by order and related topics)

In this paper, we investigate the numerical ranges of conjugations and antilinear operators on a Hilbert space, which will be shown to be annuli in general. This result proves that Toeplitz-Hausdorff Theorem, which says the convexity on the numerical ranges of linear operators, does not hold for the ones of antilinear operators. Moreover, we extend these results to a Banach space

A remark on the slice map problem

It is shown that there exist a σ-weakly closed operator algebra A˜, generated by finite rank operators and a σ-weakly closed operator algebra B˜ generated by compact operators such that the Fubini product A˜⊗¯FB˜ contains properly A˜⊗¯B˜

n-Tuples of operators satisfying σT(AB)=σT(BA)

AbstractFor “criss-cross commuting” tuples A and B of Banach space operators we give two sufficient conditions for the spectral equality σT(AB)=σT(BA)

Complex symmetric operators and isotropic vectors in Banach spaces via linear functionals (Research on structure of operators by order and related topics)

We generalize the concept of complex symmetric operators to Banach spaces via their dual spaces. With this extension we show the existence of isotropic vectors on Banach spaces whose dimension is at least two and the relation between the simplicity of an eigenvalue and the non-existence of its isotropic eigenvectors. All this work is based on [M. Cho, I. Hur and J.E. Lee, Complex symmetric operators and isotropic vectors on Banach spaces, J. Math. Anal. Appl. 479 (2019), no. 1, 752-764.]

On nn-normal operators (Research on structure of operators using operator means and related topics)

Let T be a bounded linear operator on a complex Hilbert space. T is said to be n-normal if T^{*}T^{n}=T^{n}T^{*}, where T^{*} is the dual operator of T. First we explain the study of nnormal of operators given by S.A. Alzuraiqi and A.B. Patel. Next we show our results of n-normal operators