Operator inequalities of Jensen type
Year
: 2013
Abstract: We present some generalized Jensen type operator inequalities
involving sequences of self-adjoint operators. Among other things,
we prove that if f:[0, infty) to mathbb{R} is a continuous
convex function with f(0) leq 0 , then
begin{equation*}
sum_{i=1}^{n} f(C_i) leq f left( sum_{i=1}^{n}C_i right)- delta_fsum_{i=1}^{n} widetilde{C}_i leq f left( sum_{i=1}^{n}C_i right)
end{equation*}
for all operators C_i such that 0 leq C_i leq M leq sum_{i=1}^{n} C_i (i=1, ldots,n) for some scalar
M geq0 , where widetilde{C_i} = frac{1}{2} - left|frac{C_i}{M}- frac{1}{2} right| and delta_f = f(0)+f(M) - 2 f left(
frac{M}{2} right).
involving sequences of self-adjoint operators. Among other things,
we prove that if f:[0, infty) to mathbb{R} is a continuous
convex function with f(0) leq 0 , then
begin{equation*}
sum_{i=1}^{n} f(C_i) leq f left( sum_{i=1}^{n}C_i right)- delta_fsum_{i=1}^{n} widetilde{C}_i leq f left( sum_{i=1}^{n}C_i right)
end{equation*}
for all operators C_i such that 0 leq C_i leq M leq sum_{i=1}^{n} C_i (i=1, ldots,n) for some scalar
M geq0 , where widetilde{C_i} = frac{1}{2} - left|frac{C_i}{M}- frac{1}{2} right| and delta_f = f(0)+f(M) - 2 f left(
frac{M}{2} right).
Keyword(s): convex function,positive linear map,Jensen--Mercer
operator inequality,Petrovi c operator inequality
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Operator inequalities of Jensen type
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| contributor author | محمد صال مصلحیان | en |
| contributor author | Jadranka Micic | en |
| contributor author | Mohsen Kian | en |
| contributor author | Mohammad Sal Moslehian | fa |
| date accessioned | 2020-06-06T13:15:27Z | |
| date available | 2020-06-06T13:15:27Z | |
| date issued | 2013 | |
| identifier uri | https://libsearch.um.ac.ir:443/fum/handle/fum/3347875 | |
| description abstract | We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f:[0, infty) to mathbb{R} is a continuous convex function with f(0) leq 0 , then begin{equation*} sum_{i=1}^{n} f(C_i) leq f left( sum_{i=1}^{n}C_i right)- delta_fsum_{i=1}^{n} widetilde{C}_i leq f left( sum_{i=1}^{n}C_i right) end{equation*} for all operators C_i such that 0 leq C_i leq M leq sum_{i=1}^{n} C_i (i=1, ldots,n) for some scalar M geq0 , where widetilde{C_i} = frac{1}{2} - left|frac{C_i}{M}- frac{1}{2} right| and delta_f = f(0)+f(M) - 2 f left( frac{M}{2} right). | en |
| language | English | |
| title | Operator inequalities of Jensen type | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | convex function | en |
| subject keywords | positive linear map | en |
| subject keywords | Jensen--Mercer operator inequality | en |
| subject keywords | Petrovi c operator inequality | en |
| journal title | Topological Algebra and its Applications | fa |
| pages | 21-Sep | |
| journal volume | 1 | |
| journal issue | 1 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1037800.html | |
| identifier articleid | 1037800 |