Orbits in the Maximal Ideal Space of  H  ∞ | Zendy

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Orbits in the Maximal Ideal Space of H ∞

Author(s) -

Izuchi Keiji

Publication year - 1991

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/23.6.587

Subject(s) - mathematics , maximal ideal , ideal (ethics) , bounded function , closure (psychology) , rotation (mathematics) , space (punctuation) , boundary (topology) , banach space , point (geometry) , orbit (dynamics) , unit (ring theory) , combinatorics , mathematical analysis , geometry , philosophy , epistemology , linguistics , mathematics education , economics , engineering , market economy , aerospace engineering

Let H ∞ be the Banach algebra of bounded analytic functions in the open unit disc D . We can define the rotation in the maximal ideal space M ( H ∞ ). For a point x in M ( H ∞ )\ D , an orbit O ( x ) is not closed in M ( H ∞ ). It is proved that there exists a point x in M ( H ∞ ) such that x is not contained in the Shilov boundary X and cl O ( x ), the closure of O ( x ), contains X , and there exists a point y in M ( H ∞ )\( D ∪ X ) such that cl O ( y ) ⊈ X . The rotation presents many problems concerning H ∞ . The purpose of this paper is to discuss these problems.

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