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SUBNORMALITY OF S2(a, b, c, d) AND ITS BERGER MEASURE
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 Title & Authors
SUBNORMALITY OF S2(a, b, c, d) AND ITS BERGER MEASURE
Duan, Yongjiang; Ni, Jiaqi;
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 Abstract
We introduce a 2-variable weighted shift, denoted by (a, b, c, d), which arises naturally from analytic function space theory. We investigate when it is subnormal, and compute the Berger measure of it when it is subnormal. And we apply the results to investigate the relationship among 2-variable subnormal, hyponormal and 2-hyponormal weighted shifts.
 Keywords
subnormal;(a, b, c, d);Berger measure;2-variable weighted shift;hyponormal;k-hyponormal;
 Language
English
 Cited by
 References
1.
J. Conway, The Theory of Subnormal Operators, Mathematical Surveys and Monographs, vol. 36, Amer. Math. Soc., Providence, RI, 1991.

2.
R. Courant and F. John, Introduction to Calculus and Analysis Vol. 2, Springer-Verlag, New York, 1989.

3.
J. Cui and Y. Duan, Berger measure for S(a, b, c, d), J. Math. Anal. Appl. 413 (2014), no. 1, 202-211. crossref(new window)

4.
R. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Sympos. Pure Math. 51 (1990), Part 2, 69-91.

5.
R. Curto, S. Lee, and J. Yoon, k-Hyponormality of multivariable weighted shifts, J. Funct. Anal. 229 (2005), no. 2, 462-480. crossref(new window)

6.
R. Curto, Y. Poon, and J. Yoon, Subnormality of Bergman-like weighted shifts, J. Math. Anal. Appl. 308 (2005), no. 1, 334-342. crossref(new window)

7.
R. Curto and J. Yoon, Spectral pictures of 2-variable weighted shifts, C. R. Math. Acad. Sci. Paris 343 (2006), no. 9, 579-584. crossref(new window)

8.
R. Curto and J. Yoon, Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006), no. 11, 5139-5159. crossref(new window)

9.
R. Curto and J. Yoon, Propagation phenomena for hyponormal 2-variable weighted shifts, J. Operator Theory 58 (2007), no. 1, 175-203.

10.
Y. Duan and T. Qi, Weakly k-hyponormal and polynomially hyponormal commuting operator pairs, Sci. China Math. 58 (2015), no. 2, 405-422. crossref(new window)

11.
G. Exner, Aluthge transforms and n-contractivity of weighted shifts, J. Operator Theory 61 (2009), no. 2, 419-438.

12.
K. Guo, J. Hu, and X. Xu, Toeplitz algebras, subnormal tuples and rigidity on reproducing C[$z_{1}$,..., $z_{d}$]-modules, J. Funct. Anal. 210 (2004), no. 1, 214-247. crossref(new window)

13.
N. Jewell and A. Lubin, Commuting weighted shifts and analytic function theory in several variables, J. Operator Theory 1 (1979), no. 2, 207-223.

14.
A. Shields, Weighted Shift Operator and Analytic Function Theory, Math Surveys, vol. 13. Amer. Math. Soc., Providence, 1974.

15.
K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.