Geodesic
COMPACT TOEPLITZ OPERATORS WITH CONTINUOUS SYMBOLS
Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 257-261

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DOI

For any rotation-invariant positive regular Borel measure ν on the closed unit ball whose support contains the unit sphere , let L2a be the closure in L2 = L2(, dν) of all analytic polynomials. For a bounded Borel function f on , the Toeplitz operator Tf is defined by Tf(φ) = P(fφ) for φ ∈ L2a, where P is the orthogonal projection from L2 onto L2a. We show that if f is continuous on , then Tf is compact if and only if f(z) = 0 for all z on the unit sphere. This is well known when L2a is replaced by the classical Bergman or Hardy space.
DOI : 10.1017/S0017089508004679
Mots-clés : Primary 47B35 
LE, TRIEU. COMPACT TOEPLITZ OPERATORS WITH CONTINUOUS SYMBOLS. Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 257-261. doi: 10.1017/S0017089508004679
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     title = {COMPACT {TOEPLITZ} {OPERATORS} {WITH} {CONTINUOUS} {SYMBOLS}},
     journal = {Glasgow mathematical journal},
     pages = {257--261},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004679/}
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