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Spectral decomposability of rank-one perturbations of normal operators
Foias, C.,Jung, I.B.,Ko, E.,Pearcy, C. Academic Press 2011 Journal of mathematical analysis and applications Vol.375 No.2
This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoara and Foias (1968) [1].
Chevreau, B.,Jung, I.B.,Ko, E.,Pearcy, C. Academic Press 2010 Journal of mathematical analysis and applications Vol.366 No.1
In this note we introduce some new constructions of dual spaces of operators, which are, of course, at the same time, operator spaces in the sense of Pisier (2003) [12]. We exemplify the utility of these constructs by establishing, in this more general setting, a curious and little known result from the theory of dual algebras, namely from Chevreau and Pearcy (1991) [11].
Temperature-Resistant Bicelles for Structural Studies by Solid-State NMR Spectroscopy
Yamamoto, Kazutoshi,Pearcy, Paige,Lee, Dong-Kuk,Yu, Changsu,Im, Sang-Choul,Waskell, Lucy,Ramamoorthy, Ayyalusamy American Chemical Society 2015 Langmuir Vol.31 No.4
<P>Three-dimensional structure determination of membrane proteins is important to fully understand their biological functions. However, obtaining a high-resolution structure has been a major challenge mainly due to the difficulties in retaining the native folding and function of membrane proteins outside of the cellular membrane environment. These challenges are acute if the protein contains a large soluble domain, as it needs bulk water unlike the transmembrane domains of an integral membrane protein. For structural studies on such proteins either by nuclear magnetic resonance (NMR) spectroscopy or X-ray crystallography, bicelles have been demonstrated to be superior to conventional micelles, yet their temperature restrictions attributed to their thermal instabilities are a major disadvantage. Here, we report an approach to overcome this drawback through searching for an optimum combination of bicellar compositions. We demonstrate that bicelles composed of 1,2-didecanoyl-<I>sn</I>-glycero-3-phosphocholine (DDPC) and 1,2-diheptanoyl-<I>sn</I>-glycero-3-phosphocholin (DHepPC), without utilizing additional stabilizing chemicals, are quite stable and are resistant to temperature variations. These <I>temperature-resistant bicelles</I> have a robust bicellar phase and magnetic alignment over a broad range of temperatures, between −15 and 80 °C, retain the native structure of a membrane protein, and increase the sensitivity of solid-state NMR experiments performed at low temperatures. Advantages of two-dimensional separated-local field (SLF) solid-state NMR experiments at a low temperature are demonstrated on magnetically aligned bicelles containing an electron carrier membrane protein, cytochrome <I>b</I><SUB>5</SUB>. Morphological information on different DDPC-based bicellar compositions, varying <I>q</I> ratio/size, and hydration levels obtained from <SUP>31</SUP>P NMR experiments in this study is also beneficial for a variety of biophysical and spectroscopic techniques, including solution NMR and magic-angle-spinning (MAS) NMR for a wide range of temperatures.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/langd5/2015/langd5.2015.31.issue-4/la5043876/production/images/medium/la-2014-043876_0007.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/la5043876'>ACS Electronic Supporting Info</A></P>
A Class of Invertible Bilateral Weighted Shifts
Jung, Il Bong,Pearcy, Carl Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.2
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.
On Common Invariant Subspaces of Operators
Il Bong Jung,Eungil Ko,Carl Pearcy 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.1
We present an equivalent formulation of the invariant subspace problem in terms of the existence of common invariant subspaces of some related operators, and then sketch how this formulation might be useful to establish the existence of invariant subspaces for all operators whose norm and spectral radius agree.
On Universal Coefficient Sequences
Il Bong Jung,Eungil Ko,Carl Pearcy 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.2
In this note we consider systems of simultaneous linear equations of the form AiX = Yi; i 2 I; where the Ai; X;and Yi are operators on Hilbert space, and we answer the question of when there exist “universal” coefficient sequences fAigi2 I with the property that for every sequence fYigi2 I there exists a solutionX = XfYi g to the above system.
A Note on the Spectral Mapping Theorem
JUNG, IL BONG,KO, EUNGIL,PEARCY, CARL 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.1
In this note we point out how a theorem of Gamelin and Garnett from function theory can be used to establish a spectral mapping theorem for an arbitrary contraction and an associated class of H^(∞)-functions.
Every Operator Almost Commutes with a Compact Operator
JUNG, IL BONG,KO, EUNGIL,PEARCY, CARL 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.2
In this note we set forth three possible definitions of the property of "almost commuting with a compact operator" and discuss an old result of W. Arveson that says that every operator on Hilbert space has the weakest of the three properties. Finally, we discuss some recent progress on the hyperinvariant subspace problem (see the bibliography), and relate it to the concept of almost commuting with a compact operator.
Hyperinvariant Subspaces for Some 2×2 Operator Matrices
Jung, Il Bong,Ko, Eungil,Pearcy, Carl Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3
The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of $2{\times}2$ operator matrices (Theorem 3.2).