HAHN-BANACH TYPE EXTENSION THEOREMS ON p-OPERATOR SPACES

作者：Lee Jung Jin^*

来源：Operators and Matrices, 2015, 9(3): 675-685.

DOI：10.7153/oam-09-40

• p-operator space
• Arveson
• Wittstock-Hahn-Banach theorem
• SQp space

Let V subset of W be two operator spaces. Arveson- Wittstock- Hahn- Banach theorem asserts that every completely contractive map phi : V -> B(H) has a completely contractive extension. (phi) over bar: W -> B(H), where B(H) denotes the space of all bounded operators from a Hilbert space H to itself. In this paper, we show that this is not in general true for p-operator spaces, that is, we show that there are p-operator spaces V subset of W, an SQp space E, and a p-completely contractive map. : V subset of B(E) such that. does not extend to a p-completely contractive map on W. Restricting E to L-p spaces, we also consider a condition on W under which every completely contractive extension. (phi) over bar: W -> B(L-p(mu)).

• 出版日期2015-9