Abstract
Let H be a separable Hilbert space and K be the ideal of compact operators on H. A T∈K is said to be in L(1,∞) if λn(T)=O(logn) for n≥2 or, equivalently, supN≥2(1/logN)∑N1λn(T)<∞, where λn(T) are the singular values (eigenvalues of |T|=(T*T)1/2). In this paper, we will give geometric conditions on several classes of operators, including Hankel and composition operators, belonging to L(1,∞). Specifically, we will show that the function space characterizing the symbols of these operators is a nonseparable Banach space which lies strictly between B1(D) and all the other holomorphic Besov spaces Bp(D)(p>1).
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