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Search Results: 1 - 10 of 2341 matches for " Tomohiro Hayashi "
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Non-commutative A-G mean inequality
Tomohiro Hayashi
Mathematics , 2008,
Abstract: In this paper we consider non-commutative analogue for the arithmeticgeometric mean inequality $$a^{r}b^{1-r}+(r-1)b\geq ra$$ for two positive numbers $a,b$ and $r> 1$. We show that under some assumptions the non-commutative analogue for $a^{r}b^{1-r}$ which satisfies this inequality is unique and equal to $r$-mean. The case $0
On cocycle actions of non-commutative Bernoulli shifts
Tomohiro Hayashi
Mathematics , 2005,
Abstract: This paper has been withdrawn by the author.
A note on Jensen inequality for self-adjoint operators
Tomohiro Hayashi
Mathematics , 2009,
Abstract: In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.
A note on rigidity for crossed product von Neumann algebras
Tomohiro Hayashi
Mathematics , 2006,
Abstract: In this note, we will point out, as a corollary of Popa's rigidity theory, that the crossed product von Neumann algebras for Bernoulli shifts cannot have relative property T. This is an operator algebra analogue of the theorem shown by Neuhauser and Cherix-Martin-Valette for discrete groups. Our proof is different from that for groups.
A note on the Jensen inequality for self-adjoint operators. II
Tomohiro Hayashi
Mathematics , 2012,
Abstract: This is a continuation of our previous paper. We consider a certain order-like relation for positive operators on a Hilbert space. This relation is defined by using the Jensen inequality with respect to the square-root function. We show that this relation is antisymmetric if the operators are invertible.
On normalizers of $C^{*}$-subalgebras in the Cuntz algebra $\mathcal{O}_{n}$
Tomohiro Hayashi
Mathematics , 2012,
Abstract: In this paper we investigate the normalizer $\mathcal{N}_{\mathcal{O}_{n}}(A)$ of a $C^{*}$-subalgebra $A\subset \mathcal{F}_{n}$ where $\mathcal{F}_{n}$ is the canonical UHF-subalgebra of type $n^{\infty}$ in the Cuntz algebra $\mathcal{O}_{n}$. Under the assumption that the relative commutant $A'\cap \mathcal{F}_{n}$ is finite-dimensional, we show several facts for normalizers of $A$. In particular it is shown that the automorphism group $\{{\rm Ad}u|_{A}\ \ |\ u\in \mathcal{N}_{\mathcal{F}_{n}}(A)\}$ has a finite index in $\{{\rm Ad}U|_{A}\ \ |\ U\in \mathcal{N}_{\mathcal{O}_{n}}(A)\}$.
On Error Exponents in Quantum Hypothesis Testing
Tomohiro Ogawa,Masahito Hayashi
Physics , 2002,
Abstract: In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a noncommutative analogue of the Hoeffding bound, which is identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. The upper bounds also provide a simple proof of the direct part of the quantum Stein's lemma.
A New Proof of the Direct Part of Stein's Lemma in Quantum Hypothesis Testing
Tomohiro Ogawa,Masahito Hayashi
Physics , 2001,
Abstract: The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's lemma without using Hiai-Petz's theorem, along with an operator monotone function, and in addition it is also used to show a new proof of Hiai-Petz's theorem.
A characterization of The operator-valued triangle equality
Tsuyoshi Ando,Tomohiro Hayashi
Mathematics , 2005,
Abstract: We will show that for any two bounded linear operators $X,Y$ on a Hilbert space ${\frak H}$, if they satisfy the triangle equality $|X+Y|=|X|+|Y|$, there exists a partial isometry $U$ on ${\frak H}$ such that $X=U|X|$ and $Y=U|Y|$. This is a generalization of Thompson's theorem to the matrix case proved by using a trace.
On Normalizers of $C^*$-Subalgebras in the Cuntz Algebra ${\mathcal O}_n$. II
Tomohiro Hayashi,Wojciech Szymanski
Mathematics , 2015,
Abstract: We investigate subalgebras $A$ of the Cuntz algebra ${\mathcal O}_n$ that arise as finite direct sums of corners of the UHF-subalgebra ${\mathcal F}_n$. For such an $A$, we completely determine its normalizer group inside ${\mathcal O}_n$.
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