Schatten p-norm inequalities related to an extended operator parallelogram law
سال
: 2011
چکیده: Let mathcal{C}_p be the Schatten p -class for p>0 .
Generalizations of the parallelogram law for the Schatten 2 -norms have been given in the following form:
If mathbf{A}= {A_1,A_2, ldots,A_n } and mathbf{B}= {B_1,B_2, ldots,B_n } are two sets of operators of mathcal{C}_2
sum_{i,j=1}^n |A_i-A_j |_2^2
+ sum_{i,j=1}^n |B_i-B_j |_2^2
= 2 sum_{i,j=1}^n |A_i-B_j |_2^2
- 2 Norm{ sum_{i=1}^n(A_i-B_i)}_2^2.
In this paper, we give generalizations of this as pairs of inequalities for Schatten p -norms,
which hold for certain values of $p$ and reduce to the equality
above for p=2 . Moreover, we present some related inequalities for three sets of operators.
Generalizations of the parallelogram law for the Schatten 2 -norms have been given in the following form:
If mathbf{A}= {A_1,A_2, ldots,A_n } and mathbf{B}= {B_1,B_2, ldots,B_n } are two sets of operators of mathcal{C}_2
sum_{i,j=1}^n |A_i-A_j |_2^2
+ sum_{i,j=1}^n |B_i-B_j |_2^2
= 2 sum_{i,j=1}^n |A_i-B_j |_2^2
- 2 Norm{ sum_{i=1}^n(A_i-B_i)}_2^2.
In this paper, we give generalizations of this as pairs of inequalities for Schatten p -norms,
which hold for certain values of $p$ and reduce to the equality
above for p=2 . Moreover, we present some related inequalities for three sets of operators.
کلیدواژه(گان): Schatten $p$-norm,norm inequality,parallelogram law,inner product space
کالکشن
:
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آمار بازدید
Schatten p-norm inequalities related to an extended operator parallelogram law
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| contributor author | محمد صال مصلحیان | en |
| contributor author | Masaru Tominaga | en |
| contributor author | Kichi-Suke Saito | en |
| contributor author | Mohammad Sal Moslehian | fa |
| date accessioned | 2020-06-06T14:34:03Z | |
| date available | 2020-06-06T14:34:03Z | |
| date issued | 2011 | |
| identifier uri | http://libsearch.um.ac.ir:80/fum/handle/fum/3402164 | |
| description abstract | Let mathcal{C}_p be the Schatten p -class for p>0 . Generalizations of the parallelogram law for the Schatten 2 -norms have been given in the following form: If mathbf{A}= {A_1,A_2, ldots,A_n } and mathbf{B}= {B_1,B_2, ldots,B_n } are two sets of operators of mathcal{C}_2 sum_{i,j=1}^n |A_i-A_j |_2^2 + sum_{i,j=1}^n |B_i-B_j |_2^2 = 2 sum_{i,j=1}^n |A_i-B_j |_2^2 - 2 Norm{ sum_{i=1}^n(A_i-B_i)}_2^2. In this paper, we give generalizations of this as pairs of inequalities for Schatten p -norms, which hold for certain values of $p$ and reduce to the equality above for p=2 . Moreover, we present some related inequalities for three sets of operators. | en |
| language | English | |
| title | Schatten p-norm inequalities related to an extended operator parallelogram law | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | Schatten $p$-norm | en |
| subject keywords | norm inequality | en |
| subject keywords | parallelogram law | en |
| subject keywords | inner product space | en |
| journal title | Linear Algebra and its Applications | en |
| journal title | Linear Algebra and its Applications | fa |
| pages | 823-829 | |
| journal volume | 435 | |
| journal issue | 4 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1019780.html | |
| identifier articleid | 1019780 |