• Title, Summary, Keyword: invariant subspaces

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REDUCING SUBSPACES OF WEIGHTED SHIFTS WITH OPERATOR WEIGHTS

  • Gu, Caixing
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1471-1481
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    • 2016
  • We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

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.

ZERO BASED INVARIANT SUBSPACES AND FRINGE OPERATORS OVER THE BIDISK

  • Izuchi, Kei Ji;Izuchi, Kou Hei;Izuchi, Yuko
    • Journal of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.847-868
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    • 2016
  • Let M be an invariant subspace of $H^2$ over the bidisk. Associated with M, we have the fringe operator $F^M_z$ on $M{\ominus}{\omega}M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces M. Also ker $F^M_z$ and ker $(F^M_z)^*$ are described.

INFINITELY MANY SOLUTIONS FOR A CLASS OF THE ELLIPTIC SYSTEMS WITH EVEN FUNCTIONALS

  • Choi, Q-Heung;Jung, Tacksun
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.821-833
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    • 2017
  • We get a result that shows the existence of infinitely many solutions for a class of the elliptic systems involving subcritical Sobolev exponents nonlinear terms with even functionals on the bounded domain with smooth boundary. We get this result by variational method and critical point theory induced from invariant subspaces and invariant functional.

SOME INVARIANT SUBSPACES FOR SUBSCALAR OPERATORS

  • Yoo, Jong-Kwang
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1129-1135
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    • 2011
  • In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

QUASI-INNER FUNCTIONS OF A GENERALIZED BEURLING'S THEOREM

  • Kim, Yun-Su
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1229-1236
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    • 2009
  • We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES

  • DUGGAL, B.P.;KUBRUSLY, C.S.;LEVAN, N.
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.169-177
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    • 2005
  • A Hilbert Space operator T is of class Q if $T^2{\ast}T^2-2T{\ast}T + I$ is nonnegative. Every paranormal operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if a class-Q contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = $T^2{\ast}T^2-2T{\ast}T + I$ also is a proper contraction.