Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Norms of Hankel operators on a bidisc


Author: Takahiko Nakazi
Journal: Proc. Amer. Math. Soc. 108 (1990), 715-719
MSC: Primary 47B35; Secondary 32A35, 47A30
DOI: https://doi.org/10.1090/S0002-9939-1990-1000162-5
Erratum: Proc. Amer. Math. Soc. 115 (1992), null.
MathSciNet review: 1000162
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the Hardy space on the bidisc $ {T^2}$, if $ \phi $ is a bounded function in the Lebesgue space and if its Fourier series vanishes on half of $ {{\mathbf{Z}}^2}$, then the norm of the Hankel operator $ {H_\phi }$ is equal to the quotient norm of $ \phi $ by the Hardy space $ {H^\infty }({T^2})$.


References [Enhancements On Off] (What's this?)

  • [1] S. Axler, I. D. Berg, N. Jewell and A. Shields, Approximation by compact operators and the space $ {H^\infty } + C$, Ann. of Math. 109 (1979), 601 612. MR 534765 (81h:30053)
  • [2] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611-635. MR 0412721 (54:843)
  • [3] R. E. Curto, P. S. Muhly and T. Nakazi, Uniform algebras, Hankel operators and invariant subspaces, Oper. Theory: Adv. Appl. 17 (1986), 109-119. MR 901063 (89a:46113)
  • [4] R. E. Curto, P. S. Muhly, T. Nakazi and J. Xia, Hankel operators and uniform algebras, Archiv der Math. 43 (1984), 440-447. MR 773193 (86c:47032)
  • [5] T. Nakazi, Extended weak$ ^{ - *}$ Dirichlet algebras, Pacific J. Math. 81 (1979), 493-513. MR 547616 (82a:46055)
  • [6] -, Norms of Hankel operators and uniform algebras, Trans. Amer. Math. Soc. 299 (1987), 573-580. MR 869222 (88d:47040)
  • [7] Z. Nehari, On bounded bilinear forms, Ann. of Math. 65 (1957), 153-162. MR 0082945 (18:633f)
  • [8] S. C. Power, Hankel operators on Hilbert space, Research Notes in Math. 64, Pitman, Boston, 1982. MR 666699 (84e:47037)
  • [9] A. Uchiyama, On the compactness of operators of Hankel type, Tohoku Math. J. 30 (1978), 163-171. MR 0467384 (57:7243)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B35, 32A35, 47A30

Retrieve articles in all journals with MSC: 47B35, 32A35, 47A30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1000162-5
Keywords: bidisc, Hardy space, Hankel operator, norm
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society