scholarly journals Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Miguel Antonio Morales-Ramos ◽  
Raul Quiroga-Barranco ◽  
Armando Sanchez-Nungaray
Keyword(s):  
Projective Space ◽  
Unit Ball ◽  
Complex Projective Space ◽  
Toeplitz Operators ◽  
Banach Algebras ◽  
Geometric Interpretation ◽  
Moment Maps ◽  
New Family ◽  
Commutative Banach Algebras ◽  
Complex Projective

Following previous works for the unit ball due to Nikolai Vasilevski, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudo-homogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball.

scholarly journals Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Alma García ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Weighted Bergman Space ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Extra Condition ◽  
Dimensional Unit ◽  
Commutative Banach Algebras

We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.

Toeplitz operators with quasi-separately radial symbols on the complex projective space

2015 ◽  
Vol 22 (1) ◽  
pp. 213-227
Author(s):  
Miguel A. Morales-Ramos ◽  
Armando Sánchez-Nungaray ◽  
Josué Ramírez-Ortega
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Toeplitz Operators ◽  
Complex Projective

A NOTE ON MOMENT MAPS AND KÄHLER–EINSTEIN MANIFOLDS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1215-1219 ◽  
Author(s):  
FABIO PODESTÀ
Keyword(s):  
Projective Space ◽  
Lie Group ◽  
Complex Projective Space ◽  
Einstein Manifold ◽  
Compact Lie Group ◽  
Einstein Manifolds ◽  
Moment Maps ◽  
Kähler Form ◽  
The Moment ◽  
Complex Projective

We collect some properties of the moment map relative to the isometric and holomorphic action of a compact Lie group G on a (compact) Kähler (Einstein) manifold; in particular, we study some invariants which only depend on the cohomology class of the invariant Kähler form and then specialize to the complex projective space when the group G is simple and acts linearly.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

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