multiplicative functionals
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2019 ◽  
Vol 11 (2) ◽  
pp. 311-320 ◽  
Author(s):  
S.I. Halushchak

In this work, we investigate the properties of the topological algebra of entire functions of bounded type, generated by a countable set of homogeneous polynomials on a complex Banach space. Let $X$ be a complex Banach space. We consider a subalgebra $H_{b\mathbb{P}}(X)$ of the Fréchet algebra of entire functions of bounded type $H_b(X),$ generated by a countable set of algebraically independent homogeneous polynomials $\mathbb{P}.$ We show that each term of the Taylor series expansion of entire function, which belongs to the algebra $H_{b\mathbb{P}}(X),$ is an algebraic combination of elements of $\mathbb{P}.$ We generalize the theorem for computing the radius function of a linear functional on the case of arbitrary subalgebra of the algebra $H_b(X)$ on the space $X.$ Every continuous linear multiplicative functional, acting from $H_{b\mathbb{P}}(X)$ to $\mathbb{C}$ is uniquely determined by the sequence of its values on the elements of $\mathbb{P}.$ Consequently, there is a bijection between the spectrum (the set of all continuous linear multiplicative functionals) of the algebra $H_{b\mathbb{P}}(X)$ and some set of sequences of complex numbers. We prove the upper estimate for sequences of this set. Also we show that every function that belongs to the algebra $H_{b\mathbb{P}}(X),$ where $X$ is a closed subspace of the space $\ell_{\infty}$ such that $X$ contains the space $c_{00},$ can be uniquely analytically extended to $\ell_{\infty}$ and algebras $H_{b\mathbb{P}}(X)$ and $H_{b\mathbb{P}}(\ell)$ are isometrically isomorphic. We describe the spectrum of the algebra $H_{b\mathbb{P}}(X)$ in this case for some special form of the set $\mathbb{P}.$ Results of the paper can be used for investigations of the algebra of symmetric analytic functions on Banach spaces.



2015 ◽  
Vol 13 (4) ◽  
pp. 1907-1920
Author(s):  
H. Shayanpour ◽  
E. Ansari-Piri ◽  
Z. Heidarpour ◽  
A. Zohri


2015 ◽  
Vol 51 (1) ◽  
pp. 28-58 ◽  
Author(s):  
Alexei Borodin ◽  
Ivan Corwin ◽  
Daniel Remenik


2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Włodzimierz Fechner

We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operatorsT:CX→CY, whereXandYare compact Hausdorff spaces.



2013 ◽  
Vol 95 (1) ◽  
pp. 36-67 ◽  
Author(s):  
YEMON CHOI

AbstractWe investigate which weighted convolution algebras ${ \ell }_{\omega }^{1} (S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson [‘Approximately multiplicative functionals’, J. Lond. Math. Soc. (2) 34(3) (1986), 489–510]. We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, as are all ${ \ell }_{\omega }^{1} (S)$ where $S$ has either finite width or finite height. Some of these finite-width examples are isomorphic to function algebras studied by Feinstein [‘Strong Ditkin algebras without bounded relative units’, Int. J. Math. Math. Sci. 22(2) (1999), 437–443]. We also investigate when $({ \ell }_{\omega }^{1} (S), { \mathbb{M} }_{2} )$ is an AMNM pair in the sense of Johnson [‘Approximately multiplicative maps between Banach algebras’, J. Lond. Math. Soc. (2) 37(2) (1988), 294–316], where ${ \mathbb{M} }_{2} $ denotes the algebra of $2\times 2$ complex matrices. In particular, we obtain the following two contrasting results: (i) for many nontrivial weights on the totally ordered semilattice ${ \mathbb{N} }_{\min } $, the pair $({ \ell }_{\omega }^{1} ({ \mathbb{N} }_{\min } ), { \mathbb{M} }_{2} )$ is not AMNM; (ii) for any semilattice $S$, the pair $({\ell }^{1} (S), { \mathbb{M} }_{2} )$ is AMNM. The latter result requires a detailed analysis of approximately commuting, approximately idempotent $2\times 2$ matrices.



2012 ◽  
Vol 67 (1) ◽  
pp. 181-182 ◽  
Author(s):  
Aleksandr I Bufetov


2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
F. Ershad ◽  
S. H. Petroudi

We characterize the conditions under which approximately multiplicative functionals are near multiplicative functionals on weighted Hardy spaces.



2009 ◽  
Vol 2009 (1) ◽  
pp. 486375
Author(s):  
Takeshi Miura ◽  
Hiroyuki Takagi ◽  
Makoto Tsukada ◽  
Sin-Ei Takahasi


2008 ◽  
pp. 787-804 ◽  
Author(s):  
K. L. CHUNG ◽  
K. M. RAO


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