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Operator Radii and Unitary Operators
"... Abstract. Let ρ ≥ 1 and wρ(A) be the operator radius of a linear operator A. Suppose m is a positive integer. It is shown that for a given invertible linear operator A acting on a Hilbert space, one has wρ(A −m) ≥ wρ(A) −m. The equality holds if and only if A is a multiple of a unitary operator. ..."
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Abstract. Let ρ ≥ 1 and wρ(A) be the operator radius of a linear operator A. Suppose m is a positive integer. It is shown that for a given invertible linear operator A acting on a Hilbert space, one has wρ(A −m) ≥ wρ(A) −m. The equality holds if and only if A is a multiple of a unitary operator.
NonArchimedean unitary operators
 Meth. Funct. Anal. Topology
"... Abstract. We describe a subclass of the class of normal operators on Banach spaces over nonArchimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem ab ..."
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Abstract. We describe a subclass of the class of normal operators on Banach spaces over nonArchimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem
Commutator methods for unitary operators
, 2012
"... We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local niteness of point spectrum. Large families of locally smooth ..."
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We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local niteness of point spectrum. Large families of locally smooth
Unitary Operators in Inversion
, 1997
"... this report (Nichols et al., 1992). Finally, I wish to cite another example of operator factorization for the inverse needed by (7). That example is the twodimensional predictionerror operator in Abma and Claerbout, (Abma and Claerbout, 1992). The confusion caused by that paper at the 1992 SEP spo ..."
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sponsor meeting is one reason I prepared this short note. The other reason, is to bring up again our lack of systematic use of preconditioning when we attack huge inverse problems. To begin with, I believe that the practical search for unitary operators is closely related to the practical search
MEANS OF UNITARY OPERATORS, REVISITED
, 2007
"... Abstract It is proved that an operator with bound not exceeding (n − 2)n −1 in a C * algebra is the mean of n unitay operators in that algebra. ..."
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Abstract It is proved that an operator with bound not exceeding (n − 2)n −1 in a C * algebra is the mean of n unitay operators in that algebra.
On the dynamics of a general unitary operator
 Reports on Mathematical Physics
, 1997
"... A unitary operator U acting on the weakly compact unit ball B of a Hilbert space H gives a topological dynamical system (B, V). We prove in this note that for every ergodic uinvariant measure m, the dynamical system (B, U, m) is conjugated to a strictly ergodic group translation. Especially, the to ..."
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A unitary operator U acting on the weakly compact unit ball B of a Hilbert space H gives a topological dynamical system (B, V). We prove in this note that for every ergodic uinvariant measure m, the dynamical system (B, U, m) is conjugated to a strictly ergodic group translation. Especially
Hamiltonian simulation using linear combinations of unitary operations
 Quantum Information and Computation
, 2012
"... We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, sc ..."
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We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably
Results 1  10
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2,299