Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2012 | 211 | 3 | 269-286

## The ideal of p-compact operators: a tensor product approach

EN

### Abstrakty

EN
We study the space of p-compact operators, $𝓚_{p}$, using the theory of tensor norms and operator ideals. We prove that $𝓚_{p}$ is associated to $/d_{p}$, the left injective associate of the Chevet-Saphar tensor norm $d_{p}$ (which is equal to $g_{p'}'$). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that $𝓚_{p}(E;F)$ is equal to $𝓚_{q}(E;F)$ for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of $𝓚_{p}$. For instance, we show that $𝓚_{p}$ is regular, surjective, and totally accessible, and we characterize its maximal hull $𝓚_{p}^{max}$ as the dual ideal of p-summing operators, $Π_{p}^{dual}$. Furthermore, we prove that $𝓚_{p}$ coincides isometrically with $𝓠𝓝_{p}^{dual}$, the dual to the ideal of the quasi p-nuclear operators.

269-286

wydano
2012

### Twórcy

autor
• Departamento de Matemática - Pab. I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
autor
• Departamento de Matemática - Pab. I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
autor
• Departamento de Matemática - Pab. I, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina