• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.609-620
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• 1995

In this paper, we introduce the generalization $A^{(2)}_{2n}$ of tridiagonal algebras $A_{2n}$ and investigate the isometries of such algebras.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.75-78
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• 1997

We show that if a simple $C^*$-algebra A satisfies certain $K_1$-group conditions, then two unitarily equivalent projections are homotopic. Also we show that the equivalence of projections determined by a dimension function is a homotopy.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.345-370
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• 1997

In this paper, we introduce the Fock representation $U^{F, M}$ of the Heisenberg group $H_R^(g, h)$ associated with a positive definite symmetric half-integral matrix $M$ of degree h and prove that $U^{F, M}$ is unitarily equivalent to the Schrodinger representation of index $M$.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.11-38
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• 1991

Let $E_n$ be the real ordered space of all $n{\times}n$ Hermitian Matrices and let T be a positive linear operator from $E_2$ to $E_3$. We prove in this paper that T is extreme if and only if T is unitarily equivalent to a map of the form $S_z$ for some $z{\in}C^2$ where $S_z$ is defined by $S_z(xx^*)=ww^*$, $w_i=x_iz_i$ for i = 1, 2 and $w_3=0$.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.653-659
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• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.185-189
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• 2013

In this note we study a class of invertible weighted bilateral shifts on Hilbert space introduced by Haskell Rosenthal recently. We show that every Rosenthal shift is unitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivial hyperinvariant subspace.