• 제목/요약/키워드: Hilbert ball

검색결과 4건 처리시간 0.014초

CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS

  • Kim, Kang-Tae;Ma, Daowei
    • 대한수학회지
    • /
    • 제40권3호
    • /
    • pp.503-516
    • /
    • 2003
  • We show in this paper that every domain in a separable Hilbert space, say H, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz [10] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.

The state space of a canonical linear system

  • Yang, Mee-Hyea
    • 대한수학회지
    • /
    • 제32권3호
    • /
    • pp.447-459
    • /
    • 1995
  • A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

  • PDF

REDUCING SUBSPACES OF A CLASS OF MULTIPLICATION OPERATORS

  • Liu, Bin;Shi, Yanyue
    • 대한수학회보
    • /
    • 제54권4호
    • /
    • pp.1443-1455
    • /
    • 2017
  • Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS

  • Revesz, Szilard-Gy.;Sarantopoulos, Yannis
    • 대한수학회지
    • /
    • 제41권1호
    • /
    • pp.157-174
    • /
    • 2004
  • In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.