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Positive transformations restricted to subspaces and inequalities among their proper values

Authors: A. R. Amir-Moéz and C. R. Perry
Journal: Proc. Amer. Math. Soc. 32 (1972), 363-367
MSC: Primary 15.60
MathSciNet review: 0289537
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Abstract: Let A be a positive Hermitian transformation on an n-dimensional unitary space $ {E_n}$ with proper values $ {a_1} \geqq \cdots \geqq {a_n}$. Let $ {b_1} \geqq \cdots \geqq {b_k}$ be the proper values of $ A\vert M$, where M is a proper subspace of $ {E_n}$ and $ {c_1} \geqq \cdots \geqq {c_h}$ be the proper values of $ A\vert{M^ \bot }$. Let $ {i_1} < \cdots < {i_r}$ and $ {j_1} < \cdots < {j_r}$ be sequences of positive integers, with $ {i_r} \leqq k$ and $ {j_r} \leqq h$. Then $ ({b_{{i_1}}} \cdots {b_{{i_r}}}) \cdot ({c_{{j_1}}} \cdots {c_{{j_r}}}) \geqq ... ...- r + 1}} \cdots {a_n})({a_{{i_1} + {j_1} - 1}} \cdots {a_{{i_r} + {j_r} - 1}})$. In this article generalizations of this inequality have been studied.

References [Enhancements On Off] (What's this?)

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Keywords: Positive transformations restricted to subspaces, inequalities involving proper values
Article copyright: © Copyright 1972 American Mathematical Society