scholarly journals Banach Spaces of Universal Taylor Series in the Disc Algebra

2016 ◽  
Vol 86 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Luis Bernal-González ◽  
Andreas Jung ◽  
Jürgen Müller
Keyword(s):  
Banach Spaces ◽  
Taylor Series ◽  
Disc Algebra ◽  
Universal Taylor Series

scholarly journals THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

2006 ◽  
Vol 49 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Yun Sung Choi ◽  
Domingo Garcia ◽  
Sung Guen Kim ◽  
Manuel Maestre
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Banach Spaces ◽  
Compact Space ◽  
Linear Operators ◽  
Homogeneous Polynomials ◽  
Numerical Radius ◽  
Disc Algebra ◽  
Multilinear Maps ◽  
Numerical Index

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

scholarly journals Universal Taylor series for non-simply connected domains

2010 ◽  
Vol 348 (9-10) ◽  
pp. 521-524 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Nikolaos Tsirivas
Keyword(s):  
Taylor Series ◽  
Universal Taylor Series ◽  
Simply Connected ◽  
Simply Connected Domains

Boundary Behavior of Universal Taylor Series and Their Derivatives

2005 ◽  
Vol 24 (1) ◽  
pp. 1-15 ◽  
Author(s):  
David H. Armitage ◽  
George Costakis
Keyword(s):  
Taylor Series ◽  
Boundary Behavior ◽  
Universal Taylor Series

Universal Taylor series on non-simply connected domains

Analysis ◽  
2007 ◽  
Vol 26 (3) ◽  
pp. 347-363 ◽  
Author(s):  
George Costakis ◽  
Vagia Vlachou
Keyword(s):  
Taylor Series ◽  
Universal Taylor Series ◽  
Simply Connected ◽  
Simply Connected Domains

Some remarks on universal functions and Taylor series

2000 ◽  
Vol 128 (1) ◽  
pp. 157-175 ◽  
Author(s):  
G. COSTAKIS
Keyword(s):  
Complex Plane ◽  
Taylor Series ◽  
Connected Domain ◽  
Constructive Proof ◽  
Universal Functions ◽  
Baire’S Theorem ◽  
Simply Connected Domain ◽  
Universal Taylor Series ◽  
Simply Connected

We derive properties of universal functions and Taylor series in domains of the complex plane. For some of our results we use Baire's theorem. We also give a constructive proof, avoiding Baire's theorem, of the existence of universal Taylor series in any arbitrary simply connected domain.

scholarly journals Boundary behaviour of universal Taylor series

2014 ◽  
Vol 352 (2) ◽  
pp. 99-103 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Dmitry Khavinson
Keyword(s):  
Taylor Series ◽  
Boundary Behaviour ◽  
Universal Taylor Series
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