• 호남수학학술지
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• 제36권4호
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• pp.901-906
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• 2014

In this note we provide a concrete description on the invariant subspaces for the backward shift on the Hardy space $H^2(\mathbb{T})$.

• 대한수학회보
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• 제40권4호
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• pp.693-698
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• 2003

Various operator relationships are shown to be equivalent to the existence of an invariant subspace for an algebra of operators.

• 대한수학회보
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• 제53권5호
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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.

• 대한수학회지
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• 제54권3호
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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.

• 대한수학회지
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• 제53권4호
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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.

• 대한수학회지
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• 제41권4호
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• pp.773-773
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• 2004

In our paper "Paranormal contractions and invariant subspaces" published in Journal of the Korean Mathematical Society, Volume 40 (2003), Number 6, pp.933-942, the statement to observation (1) on page 935 should read:(omitted)

• 대한수학회보
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• 제42권1호
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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.

• 대한수학회보
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• 제48권6호
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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.

• 대한수학회보
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• 제46권6호
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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.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.173-184
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• 2022

We investigated the invariant subspaces of the fractional integral operator in the Sobolev space W^k_p[0, 1] and prove unicellularity of the operator J^α by using the Duhamel product.