• Title, Summary, Keyword: p-quasihyponormal operator

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ON THE SUPERCLASSES OF QUASIHYPONORMAL OPERATIORS

  • Cha, Hyung-Koo;Shin, Kyo-Il;Kim, Jae-Hee
    • The Pure and Applied Mathematics
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    • v.7 no.2
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    • pp.79-86
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    • 2000
  • In this paper, we introduce the classes H(p,q,k),K(p;k) of operators determined by the Heinz-Kato-Furuta inequality and Holer-McCarthy inequality. We characterize relationship between p-quasihyponormal, $\kappa$-quasihyponormal and $\kappa$-p-quasihyponormal operators. And it is proved that every operator in K(p;1) for some $0 is paranormal.

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AN EXTENSION OF THE FUGLEDE-PUTNAM THEOREM TO p-QUASITHYPONORMAL OPERATORS

  • Lee, Mi-Young;Lee, Sang-Hun
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.319-324
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    • 1998
  • The equation AX = BX implies $A^*X\;=\;B^X$ when A and B are normal (Fuglede-Putnam theorem). In this paper, the hypotheses on A and B can be relaxed by usin a Hilbert-Schmidt operator X: Let A be p-quasihyponormal and let $B^*$ be invertible p-quasihyponormal such that AX = XB for a Hilbert-Schmidt operator X and $|||A^*|^{1-p}||{\cdot}|||B^{-1}|^{1-p}||\;{\leq}\;1$.Then $A^*X\;=\;XB^*$.

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WEYL'S TYPE THEOREMS FOR ALGEBRAICALLY (p, k)-QUASIHYPONORMAL OPERATORS

  • Rashid, Mohammad Hussein Mohammad;Noorani, Mohd Salmi Mohd
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.77-95
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    • 2012
  • For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.

QUASI SIMILARITY AND INJECTIVE p-QUASIHYPONORMAL OPERATORS

  • Woo, Young-Jin
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.653-659
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    • 2005
  • In this paper it is proved that quasisimilar n-tuples of tensor products of injective p-quasihyponormal operators have the same spectra, essential spectra and indices, respectively. And it is also proved that a Weyl n-tuple of tensor products of injective p-quasihyponormal operators can be perturbed by an n-tuple of compact operators to an invertible n-tuple.

Generalized Weyl's Theorem for Some Classes of Operators

  • Mecheri, Salah
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.553-563
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    • 2006
  • Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set ${\sigma}_{B{\omega}}(A)$ of all ${\lambda}{\in}\mathbb{C}$ such that $A-{\lambda}I$ is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in [6] Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem ${\sigma}_{B{\omega}}(A)={\sigma}(A)$\E(A), and the B-Weyl spectrum ${\sigma}_{B{\omega}}(A)$ of A satisfies the spectral mapping theorem. In [51], H. Weyl proved that weyl's theorem holds for hermitian operators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators [12], and to several classes of operators including semi-normal operators ([9], [10]). Recently W. Y. Lee [35] showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han [14] have extended Lee's results to algebraically paranormal operators. In [19] the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in [5], if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above results are generalized by proving that generalizedWeyl's theorem holds for the case where A is an algebraically ($p,\;k$)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

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SOME WEAK HYPONORMAL CLASSES OF WEIGHTED COMPOSITION OPERATORS

  • Jabbarzadeh, Mohammad R.;Azimi, Mohammad R.
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.793-803
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    • 2010
  • In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^2(\cal{F})$ such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.

PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES

  • Duggal, B.P.;Kubrusly, C.S.;Levan, N.
    • Journal of the Korean Mathematical Society
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    • v.40 no.6
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    • pp.933-942
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    • 2003
  • It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T + I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.