m-Isometric tensor products

IF 0.3 Q4 MATHEMATICS
Bhagawati Prashad Duggal, I. Kim
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引用次数: 0

Abstract

Abstract Given Banach space operators S i {S}_{i} and T i {T}_{i} , i = 1 , 2 i=1,2 , we use elementary properties of the left and right multiplication operators to prove, that if the tensor products pair ( S 1 ⊗ S 2 , T 1 ⊗ T 2 ) \left({S}_{1}\otimes {S}_{2},{T}_{1}\otimes {T}_{2}) is strictly m m -isometric, i.e., Δ S 1 ⊗ S 2 , T 1 ⊗ T 2 m ( I ⊗ I ) = ∑ j = 0 m ( − 1 ) j m j ( S 1 ⊗ S 2 ) m − j ( T 1 ⊗ T 2 ) m − j = 0 {\Delta }_{{S}_{1}\otimes {S}_{2},{T}_{1}\otimes {T}_{2}}^{m}\left(I\otimes I)={\sum }_{j=0}^{m}{\left(-1)}^{j}\left(\begin{array}{c}m\\ j\end{array}\right){\left({S}_{1}\otimes {S}_{2})}^{m-j}{\left({T}_{1}\otimes {T}_{2})}^{m-j}=0 , then there exist a non-zero scalar c c and positive integers m 1 , m 2 ≤ m {m}_{1},{m}_{2}\le m such that m = m 1 + m 2 − 1 m={m}_{1}+{m}_{2}-1 , ( S 1 , c T 1 ) \left({S}_{1},c{T}_{1}) is strict- m 1 {m}_{1} -isometric and S 2 , 1 c T 2 \left({S}_{2},\frac{1}{c}{T}_{2}\right) is strict m 2 {m}_{2} -isometric.
m等轴张量积
摘要给定Banach空间算子S i{S}_{i} 和T i{T}_{i} ,i=1,2i=1,2,我们利用左、右乘法算子的初等性质证明,如果张量积对(S1⊗S2,T1 \8855;T2)\left({S}_{1} \时间{S}_{2} ,{T}_{1} \时间{T}_{2} )是严格的m-等距,即ΔS1⊗S2,T1 \8855;T2 m(i \8855 i)=∑j=0 m(−1)j m j(S1 \8855;S2)m−j(T1 \8855 ; T2)m−j=0{\Delta}_{{S}_{1} \时间{S}_{2} ,{T}_{1} \时间{T}_{2} {^{m}\left(I\otimes I)={\sum}_{j=0}^}m}}{\lefort(-1)}^{j}\lift(\ begin{array}{c}m\\j\end{array}\right){\left({S}_{1} \时间{S}_{2} )^{m-j}{\left({T}_{1} \时间{T}_{2} )}^{m-j}=0,则存在非零标量c和正整数m1,m2≤m{m}_{1} ,{m}_{2} 使m=m 1+m 2−1 m={m}_{1}+{m}_{2}-1,(S1,c T1)\左({S}_{1} ,c{T}_{1} )是严格的-m 1{m}_{1} -等距和S2,1 c T 2\left({S}_{2} ,\frac{1}{c}{T}_{2} \right)是严格的m2{m}_{2} -等距。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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