A note on the hyperreflexivity constant for certain reflexive algebras

• Autorzy: Satoru Tosaka
• Języki publikacji: EN

Abstrakty

EN

Using results on the reflexive algebra with two invariant subspaces, we calculate the hyperreflexivity constant for this algebra when the Hilbert space is two-dimensional. Then by the continuity of the angle for two subspaces, there exists a non-CSL hyperreflexive algebra with hyperreflexivity constant C for every C>1. This result leads to a kind of continuity for the hyperreflexivity constant.

Kategorie tematyczne

• 47L05: Linear spaces of operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 134
• Numer: 3
• Strony: 203-206

Daty

wydano

1999

otrzymano

1996-06-17

poprawiono

1998-11-23

Twórcy

autor

Satoru Tosaka

• Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan ,

Bibliografia

• [1] M. Anoussis, A. Katavolos and M. S. Lambrou, On the reflexive algebra with two invariant subspaces, J. Operator Theory 30 (1993), 267-299.
• [2] W. Argyros, M. S. Lambrou and W. Longstaff, Atomic Boolean subspace lattices and applications to the theory of bases, Mem. Amer. Math. Soc. 445 (1991).
• [3] W. Arveson, Ten Lectures on Operator Algebras, CBMS Regional Conf. Ser. in Math. 55, Amer. Math. Soc., Providence, 1984.
• [4] A. Katavolos, M. S. Lambrou and W. Longstaff, The decomposability of operators relative to two subspaces, Studia Math. 105 (1993), 25-36.
• [5] M. S. Lambrou and W. Longstaff, Unit ball density and the operator equation AX=YB, J. Operator Theory 25 (1991), 383-397.
• [6] M. Papadakis, On hyperreflexivity and rank one density for non-CSL algebras, Studia Math. 98 (1991), 11-17.