Pfaffian and decomposable numerical range of a complex skew symmetric matrix
نویسنده
چکیده
In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by TiT ∗ j + TjT ∗ i = 2δijI, i, j = 1, . . . , p, where δij is the Kronecker delta. The numerical radius of weighted shift operators Speaker Mao-Ting Chien (Soochow University), [email protected] Co-author Hiroshi Nakazato (Hirosaki University). Abstract Let T be a bounded linear operator on a complex Hilbert space H. For 0 ≤ q ≤ 1, the q-numerical range Wq(T ) of T is defined by Wq(T ) = {〈Tξ, η〉 : ||ξ|| = ||η|| = 1, 〈ξ, η〉 = q}. Wq(T ) is a bounded convex subset of C. Its q-numerical radius is denoted by wq(T ) = sup{|z| : z ∈Wq(T )}. If T is a weighted shift operator on `2(N) with bounded weights {sn}, it is known thatWq(T ) is a circular disk about the origin. This paper deals with computations of the the q-numerical radius of weighted shift operators with geometric weights and periodic weights.Let T be a bounded linear operator on a complex Hilbert space H. For 0 ≤ q ≤ 1, the q-numerical range Wq(T ) of T is defined by Wq(T ) = {〈Tξ, η〉 : ||ξ|| = ||η|| = 1, 〈ξ, η〉 = q}. Wq(T ) is a bounded convex subset of C. Its q-numerical radius is denoted by wq(T ) = sup{|z| : z ∈Wq(T )}. If T is a weighted shift operator on `2(N) with bounded weights {sn}, it is known thatWq(T ) is a circular disk about the origin. This paper deals with computations of the the q-numerical radius of weighted shift operators with geometric weights and periodic weights.
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