Isometric representations of calibrated ordered spaces on $C(X)$

Serdar Ay

Makale detayları

Isometric representations of calibrated ordered spaces on $C(X)$

Yazarlar:

Serdar Ay

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.523-545

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357879

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of CX, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representability as a subspace of CX for some locally compact Hausdorff space X, in the algebraic, order and seminorm sense are stated and proved. Some characterizations appear to be new even in the normed case. A recent result on isometric representations of locally ordered spaces fall under the results in this paper with more general statements. As an application of the main theorems, we state and prove a characterization of norm additivity property of two positive functionals.

 The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of CX, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representability as a subspace of CX for some locally compact Hausdorff space X, in the algebraic, order and seminorm sense are stated and proved. Some characterizations appear to be new even in the normed case. A recent result on isometric representations of locally ordered spaces fall under the results in this paper with more general statements. As an application of the main theorems, we state and prove a characterization of norm additivity property of two positive functionals.

 The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of CX, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representability as a subspace of CX for some locally compact Hausdorff space X, in the algebraic, order and seminorm sense are stated and proved. Some characterizations appear to be new even in the normed case. A recent result on isometric representations of locally ordered spaces fall under the results in this paper with more general statements. As an application of the main theorems, we state and prove a characterization of norm additivity property of two positive functionals.

 The problem of characterizing normed ordered spaces which admit a representation in the algebraic, order and norm sense as a subspace of CX, the space of all continuous functions on a compact Hausdorff space is a classical problem that has been considered by many authors. In this article we consider the more general case of calibrated ordered spaces, that is, ordered spaces with a specified family of seminorms generating its topology. For such spaces equivalent conditions on representability as a subspace of CX for some locally compact Hausdorff space X, in the algebraic, order and seminorm sense are stated and proved. Some characterizations appear to be new even in the normed case. A recent result on isometric representations of locally ordered spaces fall under the results in this paper with more general statements. As an application of the main theorems, we state and prove a characterization of norm additivity property of two positive functionals.

Makale detayları

Isometric representations of calibrated ordered spaces on $C(X)$

Yazarlar:

Serdar Ay

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.523-545

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357879

pISSN:

1303-5991

Calibrated ordered space

representation of an ordered space

locally Riesz space

Schaefer’s construction

BNN extension

Sayı

Makale detayları

Isometric representations of calibrated ordered spaces on $C(X)$

Yazarlar: Serdar Ay

Yayıncı: Ankara University

Ana Başlıklar: Operator Algebras and Functional Analysis

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.523-545

Belge Tipi: Makale

Yayın Tarihi: 9/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001357879

pISSN: 1303-5991

Calibrated ordered space

representation of an ordered space

locally Riesz space

Schaefer’s construction

BNN extension

Sayı

Yazarlar:

Serdar Ay

Yayıncı:

Ankara University

Ana Başlıklar:

Operator Algebras and Functional Analysis

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.523-545

Belge Tipi:

Makale

Yayın Tarihi:

9/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001357879

pISSN:

1303-5991