Classification of multiple unilateral weighted shifts by <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="Mml1" altimg="images\hcm0000417260.png" baseline="-6.5" display="inline" overflow="scroll"><mml:msub><mml:mstyle mathvariant="double-struck"><mml:mrow><mml:mi mathvariant="double-struck">A</mml:mi></mml:mrow></mml:mstyle><mml:msub><mml:mrow><mml:mi mathvariant="normal">?</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:msub></mml:math></inline-formula>

Juexian LI

doi:10.1007/s11464-012-0180-y

PDF(148 KB)

Front. Math. China ›› 2012, Vol. 7 ›› Issue (3) : 487-496. DOI: 10.1007/s11464-012-0180-y

RESEARCH ARTICLE

Classification of multiple unilateral weighted shifts by A?0

Juexian LI

Author information +

History +

Abstract

In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes $A n (1 ≤ n ≤ ℵ 0)$ . As a result, we perfect and generalize the previous conclusions given by H. Bercovici, C. Foias, and C. Pearcy. Moreover, we remark that Question 21 posed by Shields has been negatively answered.

Keywords

Multiple unilateral weighted shifts / classes $A n$

Cite this article

EndNote

Ris (Procite)

Bibtex

Download citation ▾

Juexian LI. Classification of multiple unilateral weighted shifts by

A ℵ 0

. Front Math Chin, 2012, 7(3): 487‒496 https://doi.org/10.1007/s11464-012-0180-y

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Bercovici H. A contribution to the structure theory of operators in the class A. J Funct Anal, 1988, 78: 197-207 CrossRef Google scholar

[2]	Bercovici H. Factorization theorem and the structure of operators on Hilbert space. Ann Math, 1988, 128: 399-413 CrossRef Google scholar

[3]	Bercovici H, Foias C, Pearcy C. Dilation theory and systems of simultaneous equations in the predual of an operator algebra I. Michigan Math J, 1983, 30: 335-354 CrossRef Google scholar

[4]	Bercovici H, Foias C, Pearcy C. Dual Algebras with Applications to Invariant Subspaces and Dilation Theory. CBMS Regional Conference Ser in Math, No 56. Providence: Amer Math Soc, 1985

[5]	Chevreau B. Sur les contractions à calcul fonctionnel isométrique. J Operator Theory, 1988, 20: 269-293

[6]	Halmos P R. A Hilbert Space Problem Book. 2nd ed. Berlin-New York: Springer- Verlag, 1982 CrossRef Google scholar

[7]	Herrero D A. The Fredholm structure of on n-multicyclic operators. Indiana Univ Math J, 1987, 36: 549-566 CrossRef Google scholar

[8]	Lü F, Liu L F. The characterizations of shift operators being universal dilations. Science in China, Ser A, 1992, 35: 1017-1025 (in Chinese)

[9]	Makai E, Zemánek J. The surjectivity radius, packing numbers and boundedness below of linear operators. Integral Equations Operator Theory, 1983, 6: 372-384 CrossRef Google scholar

[10]	Shields A L. Weighted shift operators and analytic function theory. In: Topics in Operator Theory, Math Surveys, Vol 13. Providence: Amer Math Soc, 1974, 49-128