Wyniki wyszukiwania

1

Structure spaces for rings of continuous functions with applications to realcompactifications

100%

Redlin L., Watson S.

Fundamenta Mathematicae

|

1997

|

tom 152

|

nr 2

151-163

EN

Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).

2

A local algebra structure for $H^p$ of the polydisc

100%

Merryfield K. G., Watson S.

Colloquium Mathematicum

|

1991

|

tom 62

|

nr 1

73-79

3

A multiplier theorem for Fourier series in several variables

81%

Asmar N., Newberger F., Watson S.

Colloquium Mathematicum

|

2006

|

tom 106

|

nr 2

221-230

EN

We define a new type of multiplier operators on $L^{p}(𝕋^N)$, where $𝕋^N$ is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on $L^{p}(𝕋^N)$, to which the theorem applies as a particular example.

4

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Correspondences between ideals and $z$-filters for rings of continuous functions between $C^∗$ and $C$

81%

Panman P., Sack J., Watson S.

Commentationes Mathematicae

|

2012

|

tom 52

|

nr 1

EN

Let $X$ be a completely regular topological space. Let $A(X)$ be a ring of continuous functions between $C^∗(X)$ and $C(X)$, that is, $C^∗(X) \subset A(X) \subset C(X)$. In [9], a correspondence $\mathcal{Z}_A$ between ideals of $A(X)$ and $z$-filters on $X$ is defined. Here we show that $\mathcal{Z}_A$ extends the well-known correspondence for $C^∗(X)$ to all rings $A(X)$. We define a new correspondence $\mathcal{Z}_A$ and show that it extends the well-known correspondence for $C(X)$ to all rings $A(X)$. We give a formula that relates the two correspondences. We use properties of $\mathcal{Z}_A$ and $\mathcal{Z}_A$ to characterize $C^∗(X)$ and $C(X)$ among all rings $A(X)$. We show that $\mathcal{Z}_A$ defines a one-one correspondence between maximal ideals in $A(X)$ and the $z$-ultrafilters in $X$.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Commentationes Mathematicae

1 Fundamenta Mathematicae

4 Watson S.

1 Asmar N.

1 Merryfield K. G.

1 Newberger F.

1 Panman P.

1 Redlin L.

1 Sack J.

1 2012

1 2006

1 1997

1 1991

Structure spaces for rings of continuous functions with applications to realcompactifications

A local algebra structure for $H^p$ of the polydisc

A multiplier theorem for Fourier series in several variables

Correspondences between ideals and \(z\)-filters for rings of continuous functions between \(C^∗\) and \(C\)