The numerical ranges of unbounded linear operators
نویسندگان
چکیده
منابع مشابه
Tracial Numerical Ranges and Linear Dependence of Operators
Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.
متن کاملEla Tracial Numerical Ranges and Linear Dependence of Operators
Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.
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Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 i...
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It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the essential numerical range. The latter is described quantitatively, and based on that sufficient conditions are established under which the c-numerical range also is an ellipse. Several examples are considered, including singular integral operators with the Cauchy kernel...
متن کاملLinear maps transforming the higher numerical ranges
Let k ∈ {1, . . . , n}. The k-numerical range of A ∈Mn is the set Wk(A) = {(trX∗AX)/k : X is n× k, X∗X = Ik}, and the k-numerical radius of A is the quantity wk(A) = max{|z| : z ∈ Wk(A)}. Suppose k > 1, k′ ∈ {1, . . . , n′} and n′ < C(n, k)min{k′, n′ − k′}. It is shown that there is a linear map φ : Mn → Mn′ satisfying Wk′(φ(A)) = Wk(A) for all A ∈ Mn if and only if n′/n = k′/k or n′/n = k′/(n−...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1975
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700023601