Quadratic forms in unitary operators

Details Quadratic forms in unitary operators Quadratic forms in unitary operators

1995-12-14

arxiv.org/abs/math/9512207v1

Linear Algebra and its Applications. 267 (1997) 125-137.

Mathematics

Functional Analysis

Scientific paper

Let $u_1,\ldots,u_n$ be unitary operators on a Hilbert space $H$. We study the norm $$\left\|\sum^{i=n}_{i=1} u_i \otimes \bar u_i\right\|\leqno (1)$$ of the operator $\sum u_i \otimes \bar u_i$ acting on the Hilbertian tensor product $H\otimes_2 \overline H$. The main result of this note is Theorem 1. For any $n$-tuple $u_1,\ldots, u_n$ of unitary operators in $B(H)$, we have $$2\sqrt{n-1} \le \left\|\sum^n_1 u_i \otimes \bar u_i\right\|.\leqno (6)$$ In other words, the right side of (6) is minimal exactly when $u_i = \lambda(g_i)$.

Affiliated with

Also associated with

No associations

Rating

Quadratic forms in unitary operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quadratic forms in unitary operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quadratic forms in unitary operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-651519