Papers by Shizuo Miyajima
A bounded linear operator T is called ∞-hyponormal if T is p-hyponormal for every p> 0. In thi... more A bounded linear operator T is called ∞-hyponormal if T is p-hyponormal for every p> 0. In this paper ∞-hyponormality of the Aluthge transformations of ∞-hyponormal operators is investigated. It is shown that the Aluthge transfor- mation of an ∞-hyponormal operator is not necessarily ∞-hyponormal. It is also shown that the (generalized) Aluthge transformation of an ∞-hyponormal operator T is ∞-hyponormal provided |T ||T ∗ | = |T ∗ ||T |. Moreover we give an example of an ∞-hyponormal operator T whose Aluthge transformation ˜ T is ∞-hyponormal but |T ||T ∗ | � |T ∗ ||T |.
SUT Journal of Mathematics
Recently, it has been revealed that the semigroups satisfying Gaussian estimates inherit some of ... more Recently, it has been revealed that the semigroups satisfying Gaussian estimates inherit some of the nice properties enjoyed by the Gaussian semigroup itself. Arendt [1] gives a result in this direction, by proving the invariance of the spectrum of the generators of consistent C0-semigroups with Gaussian estimates. In this paper, we generalize this result to the semigroups estimated by the one generated by the fractional power −(I − ∆) α (1/2 < α ≤ 1).
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Papers by Shizuo Miyajima