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A Characterization of Pick Bodies
Author(s) -
Cole B.,
Lewis K.,
Wermer J.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.2.316
Subject(s) - characterization (materials science) , hilbert space , unit disk , tuple , unit (ring theory) , space (punctuation) , pure mathematics , mathematics , combinatorics , physics , computer science , discrete mathematics , optics , mathematics education , operating system
Let z = ( z 1 …, z n ) be an n ‐tuple of distinct points in the open unit disk. We define the Pick body D ;( z ) as the totality of points w = ( w 1 ,…, w n ) in C n such that there exists f € H ∞ with ‖ f ‖ ∞ ⩽ 1 and f ( z 1 ) = w 1 , for 1 ⩽ j ⩽ n . We discuss the properties of Pick bodies and characterize them among compact subsets of C n . We also study related questions concerning certain algebras of operators on Hilbert space.