Explicit upper bounds for the spectral distance of two trace class operators
نویسندگان
چکیده
منابع مشابه
EXPLICIT UPPER BOUNDS FOR THE AVERAGE ORDER OF dn(m) AND APPLICATION TO CLASS NUMBER
In this paper, we prove some explicit upper bounds for the average order of the generalized divisor function, and, according to an idea of Lenstra, we use them to obtain bounds for the class number of number fields.
متن کاملTrace class operators and Hilbert-Schmidt operators
If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...
متن کاملExplicit and Almost Explicit Spectral Calculations for Diffusion Operators
The diffusion operator HD = − 1 2 d dx a d dx − b d dx = − 1 2 exp(−2B) d dx a exp(2B) d dx , where B(x) = R x 0 b a (y)dy, defined either on R = (0,∞) with the Dirichlet boundary condition at x = 0, or on R, can be realized as a self-adjoint operator with respect to the density exp(2Q(x))dx. The operator is unitarily equivalent to the Schrödinger-type operator HS = − 1 2 d dx a d dx + Vb,a, wh...
متن کاملUpper bounds for Stein-type operators
We present sharp bounds on the supremum norm of DjSh for j ≥ 2, where D is the differential operator and S the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with D replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the c...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.10.008