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

• Autorzy: Daniel Galicer , Silvia Lassalle , Pablo Turco
• Języki publikacji: 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.

Kategorie tematyczne

• 47L20: Operator ideals
• 46A32: Spaces of linear operators; topological tensor products; approximation properties
• 47B07: Operators defined by compactness properties
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 3
• Strony: 269-286

Daty

wydano

2012

Twórcy

autor

Daniel Galicer

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

autor

Silvia Lassalle

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

autor

Pablo Turco

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

Identyfikatory

DOI

10.4064/sm211-3-8