scholarly journals On locally convex extension of H∞in the unit ball and continuity of the Bergman projection

2003 ◽  
Vol 156 (3) ◽  
pp. 261-275 ◽  
Author(s):  
M. Jasiczak
Keyword(s):  
Unit Ball ◽  
Bergman Projection ◽  
Locally Convex

scholarly journals Weighted estimates for the Berezin transform and Bergman projection on the unit ball

2016 ◽  
Vol 286 (3-4) ◽  
pp. 1465-1478 ◽  
Author(s):  
Rob Rahm ◽  
Edgar Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Berezin Transform ◽  
Bergman Projection ◽  
Weighted Estimates

scholarly journals A Sharp Constant for the Bergman Projection

2015 ◽  
Vol 58 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Projection Operator ◽  
Bergman Projection ◽  
Hyperbolic Metric ◽  
Sharp Constant ◽  
The Hyperbolic Metric

AbstractFor the Bergman projection operator P we prove thatHere λ stands for the hyperbolic metric in the unit ball B of Cn, and B1 denotes the Besov space with an adequate semi-norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.

scholarly journals Norm of the Bergman Projection

2014 ◽  
Vol 115 (1) ◽  
pp. 143 ◽  
Author(s):  
David Kalaj ◽  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Projection Operator ◽  
Bloch Space ◽  
Bergman Projection ◽  
Invariant Norm ◽  
Weighted Bergman Projection ◽  
Special Case

This paper deals with the the norm of the weighted Bergman projection operator $P_{\alpha}:L^\infty(B)\rightarrow\mathscr{B}$ where $\alpha > - 1$ and $\mathscr{B}$ is the Bloch space of the unit ball $B$ of the $\mathsf{C}^n$. We consider two Bloch norms, the standard Bloch norm and invariant norm w.r.t. automorphisms of the unit ball. Our work contains as a special case the main result of the recent paper [6].

scholarly journals Linear operators whose domain is locally convex

1977 ◽  
Vol 20 (4) ◽  
pp. 293-299 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Linear Operators ◽  
Continuous Linear ◽  
Locally Convex

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on S separates the points of S. If X is a Banach space and T : X → F is a continuous linear operator, then T is quasi-convex if is quasi-convex, where U is the unit ball of X.

scholarly journals A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-7
Author(s):  
Yufeng Lu ◽  
Jun Yang
Keyword(s):  
Linear Operator ◽  
Unit Ball ◽  
Bounded Linear Operator ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Weighted Bergman Spaces ◽  
Bounded Linear ◽  
Weighted Bergman Projection

This paper shows that ifSis a bounded linear operator acting on the weighted Bergman spacesAα2on the unit ball inℂnsuch thatSTzi=Tz¯iS (i=1,…,n), whereTzi=zifandTz¯i=P(z¯if); and wherePis the weighted Bergman projection, thenSmust be a Hankel operator.

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

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