A NOTE ON CHARACTERISTIC EQUATION OF TOEPLITZ OPERATORS ON THE SPACES Ak
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چکیده
Note that μ0 is simply normalized Lebesque measure on B. The k-th Bergman space, Ak, is defined as the space of analytic functions on B which are square integrable with respect to the measure μk. Note that Ak = H (μk), where H (μk) be the L2(μk) -closure of the ball algebra A, and that Aj c Ak for j < k. The standard orthonormal base for Ak is given by eka = c(a, k, n)z a = c{a, ky n)r^e i0Clθl r?e where c(a, k, n) is a constant number such that c(a, k, n) || z || = 1. Let Pk denote the projection of L (μk) onto Ak. Note that L°°(μk) = L°°(B) = {/ : / i s essentially bounded on B with respect to Lebesque measure on B}. Also H°°(μk), the weak -closure of the polynomials in z in L°°(B), is the set {/ : / G L°°(B) and fAk £ i4fc} = 7/ , the set of bounded analytic functions on B. For f ^ L (B), II/L denotes the essential supremum of/ on £. For any φ ^ L°°(B) and for any /c > 0, we define a Toeplitz operator Tφ :Ak—>Ak as follows: T \ \fC) /• χ% / / \ / /• _ Λ \
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