• Title, Summary, Keyword: subnormal operators

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JOINT WEAK SUBNORMALITY OF OPERATORS

  • Lee, Jun Ik;Lee, Sang Hoon
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.2
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    • pp.287-292
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    • 2008
  • We introduce jointly weak subnormal operators. It is shown that if $T=(T_1,T_2)$ is subnormal then T is weakly subnormal and if f $T=(T_1,T_2)$ is weakly subnormal then T is hyponormal. We discuss the flatness of weak subnormal operators.

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SOLVABILITY OF SYLVESTER OPERATOR EQUATION WITH BOUNDED SUBNORMAL OPERATORS IN HILBERT SPACES

  • Bekkar, Lourabi Hariz;Mansour, Abdelouahab
    • Korean Journal of Mathematics
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    • v.27 no.2
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    • pp.515-523
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    • 2019
  • The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.

ON UNBOUNDED SUBNOMAL OPERATORS

  • Jin, Kyung-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.65-70
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    • 1993
  • In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

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Subnormality and Weighted Composition Operators on L2 Spaces

  • AZIMI, MOHAMMAD REZA
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.345-353
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    • 2015
  • Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

A Note on Subnormal and Hyponormal Derivations

  • Lauric, Vasile
    • Kyungpook Mathematical Journal
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    • v.48 no.2
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    • pp.281-286
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    • 2008
  • In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

WEAK NORMAL PROPERTIES OF PARTIAL ISOMETRIES

  • Liu, Ting;Men, Yanying;Zhu, Sen
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1489-1502
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    • 2019
  • This paper describes when a partial isometry satisfies several weak normal properties. Topics treated include quasi-normality, subnormality, hyponormality, p-hyponormality (p > 0), w-hyponormality, paranormality, normaloidity, spectraloidity, the von Neumann property and Weyl's theorem.