Essential commutant of analytic Toeplitz operators

1997 ◽  
Vol 42 (7) ◽  
pp. 548-552 ◽  
Author(s):  
Xuanhao Ding ◽  
Shunhua Sun
2011 ◽  
Vol 261 (5) ◽  
pp. 1361-1383 ◽  
Author(s):  
Michael Didas ◽  
Jörg Eschmeier ◽  
Kevin Everard

2015 ◽  
Vol 58 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Kei Hasegawa

AbstractLet α: G ↷ M be a spatial action of a countable abelian group on a “spatial” von Neumann algebra M and let S be its unital subsemigroup with G = S-1S. We explicitly compute the essential commutant and the essential fixed-points, modulo the Schatten p-class or the compact operators, of the w*-semicrossed product of M by S when M' contains no non-zero compact operators. We also prove a weaker result when M is a von Neumann algebra on a finite dimensional Hilbert space and (G, S) = (ℤ, ℤ+), which extends a famous result due to Davidson (1977) for the classical analytic Toeplitz operators.


2010 ◽  
Vol 62 (4) ◽  
pp. 889-913 ◽  
Author(s):  
Jingbo Xia

AbstractLet 𝒯 be the C*-algebra generated by the Toeplitz operators {T𝜑 : 𝜑 Є L∞(S, dσ)} on the Hardy space H2(S) of the unit sphere in Cn. It is well known that 𝒯 is contained in the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)}. We show that the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)} is strictly larger than 𝒯.


2021 ◽  
Vol 93 (3) ◽  
Author(s):  
Harald Upmeier

AbstractWe determine the eigenvalues of certain “fundamental” K-invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$ D = G / K , for the irreducible K-types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$ r = rank ( D ) .


1996 ◽  
Vol 180 (1) ◽  
pp. 299-315 ◽  
Author(s):  
E. Ram Írez De Arellano ◽  
N. L. Vasilevski

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sumin Kim ◽  
Jongrak Lee

AbstractIn this paper, we present some necessary and sufficient conditions for the hyponormality of Toeplitz operator $T_{\varphi }$ T φ on the Bergman space $A^{2}(\mathbb{D})$ A 2 ( D ) with non-harmonic symbols under certain assumptions.


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