The Adamjan‐Arov‐Krein Theorem on  H p  ‐Spaces (2 ⩽  p  ⩽ ∞) and on the Disc Algebra | Zendy

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The Adamjan‐Arov‐Krein Theorem on H p ‐Spaces (2 ⩽ p ⩽ ∞) and on the Disc Algebra

Author(s) -

Le Merdy Christian

Publication year - 1993

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/25.3.275

Subject(s) - mathematics , bilinear interpolation , extension (predicate logic) , statement (logic) , constant (computer programming) , bilinear form , pure mathematics , combinatorics , algebra over a field , discrete mathematics , law , statistics , computer science , political science , programming language

This paper is devoted to the following extension of the AAK theorem. Let ( p,q )∈[2, + ∞] 2 . Let u : H p × H q → C bea hankelian bilinear form and n ∈ N*. There is a hankelian bilinear form v : H p × H q →C with rk ( v ) < n and ∥ u − v ∥ ⩽ Ca n ( U ) for some constant C > 0 depending only on ( p,q ). Moreover, H p or H q may be replaced by A in this statement.

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