Tadasi Huruya

A note on -hyponormal operators

Let T be a p-hyponormal operator on a Hilbert space with polar decomposition T = UITI and let T = ITjtUITjr-t for r > 0 and r > t > 0. We study order and spectral properties of T. In particular we refine recent Furutas result on p-hyponormal operators.

Spectra of completely log-hyponormal operators

An operatorT on a Hilbert space is called log-hyponormal if it is invertible and log(T*T)≥log(T*T). In this paper we study spectral properties of completely log-hyponormal operators.

n-Tuples of operators satisfying σT(AB) = σT(BA)

Abstract For “criss-cross commuting” tuples A and B of Banach space operators we give two sufficient conditions for the spectral equality σ T ( AB )= σ T ( BA ).

A norm property for spaces of completely bounded maps between C*-algebras

Let M n be the C*-algebra of n × n complex matrices. If A is a C*-algebra, let M n ( A ) denote the C*-algebra of n × n matrices a = [a ij ] with entries in A . For a linear map between C*-algebras, we define the multiplicity map by A linear map O is said to be completely bounded if Let B ( A, B ), CB( A, B ) denote the Banach space of bounded linear maps, the set of completely bounded maps from A to B , respectively.

Square of ω-hyponormal operators

In this paper, we show that ifT is a ω-hyponormal operator, thenT2 is also ω-hyponormal.

A remark on numerical range of semi-hyponormal operators

Let U be the unilateral shift on ℓ2. For any complex numbers α and β, put T = αU + βU* and S = T 2. Then we show that the operator S is convexoid.

A remark on the slice map problem

It is shown that there exist a σ-weakly closed operator algebra A˜, generated by finite rank operators and a σ-weakly closed operator algebra B˜ generated by compact operators such that the Fubini product A˜⊗¯FB˜ contains properly A˜⊗¯B˜.

Separable injectivity and C*-tensor products

Let A and B be C*-algebras and let D be a C*-subalgebra of B. We show that if D is separably injective then the triple (A,B,D) verifies the slice map conjecture. As an application, we prove that the minimal C*-tensor product A⊗B is separably injective if and only if both A and B are separably injective and either A or B is finite-dimensional.