Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  Shilov boundary
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Knots in $S^2 x S^1$ derived from Sym(2, ℝ)

100%
Lee S. Y., Lim Y., Park C.-Y.
Fundamenta Mathematicae
|
2000
|
tom 164
|
nr 3
241-252
EN
We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in $S^2 × S^1$ and show that these knots or links have certain types of symmetry of period 2.
2
Content available remote

Boundaries of weak peak points in noncommutative algebras of Lipschitz functions

75%
Averill K., Johnston A., Northrup R., Silversmith R., Luttman A.
Open Mathematics
|
2012
|
tom 10
|
nr 2
646-655
EN
It has been shown that any Banach algebra satisfying ‖f 2‖ = ‖f‖2 has a representation as an algebra of quaternion-valued continuous functions. Whereas some of the classical theory of algebras of continuous complex-valued functions extends immediately to algebras of quaternion-valued functions, similar work has not been done to analyze how the theory of algebras of complex-valued Lipschitz functions extends to algebras of quaternion-valued Lipschitz functions. Denote by Lip(X, $\mathbb{F}$ ) the algebra over R of F-valued Lipschitz functions on a compact metric space (X, d), where $\mathbb{F}$ = ℝ, ℂ, or ℍ, the non-commutative division ring of quaternions. In this work, we analyze a class of subalgebras of Lip(X, $\mathbb{F}$ ) in which the closure of the weak peak points is the Shilov boundary, and we show that algebras of functions taking values in the quaternions are the most general objects to which the theory of weak peak points extends naturally. This is done by generalizing a classical result for uniform algebras, due to Bishop, which ensures the existence of the Shilov boundary. While the result of Bishop need not hold in general algebras of quaternion-valued Lipschitz functions, we give sufficient conditions on such an algebra for it to hold and to guarantee the existence of the Shilov boundary.
3
Content available remote

Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras

75%
Hatori O., Hirasawa G., Miura T.
Open Mathematics
|
2010
|
tom 8
|
nr 3
597-601
EN
Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M A and M B, respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M B → M A and a closed and open subset K of M B such that $$ \widehat{T\left( a \right)}\left( y \right) = \left\{ \begin{gathered} \widehat{T\left( e \right)}\left( y \right)\hat a\left( {\phi \left( y \right)} \right) y \in K \hfill \\ \widehat{T\left( e \right)}\left( y \right)\overline {\hat a\left( {\phi \left( y \right)} \right)} y \in M_\mathcal{B} \backslash K \hfill \\ \end{gathered} \right. $$ for all a ∈ A, where e is unit element of A. If, in addition, $$ \widehat{T\left( e \right)} = 1 $$ and $$ \widehat{T\left( {ie} \right)} = i $$ on M B, then T is an algebra isomorphism.
4
Content available remote

Pointwise multiplication operators on weighted Banach spaces of analytic functions

63%
Bonet J., Domański P., Lindström M.
Studia Mathematica
|
1999
|
tom 137
|
nr 2
177-194
EN
For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator $M_φ$, $M_φ(f)=φf$, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when $M'_φ$ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map $M'_φ$.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.