A Note on Total Antieigenvectors

On the joint antieigenvalues of operators in normal subalgebras

“…We remark that although these expressions may appear complicated, they may be clearly understood as sets analogous to those previously identified for single compact normal operators, see [9,10,14,15]. …”

“…We call µ 1 (T , S) the joint antieigenvalue of T and S. We also call a vector f for which the infimum in (2) is attained a joint antieigenvector of T and S. The author and Karl Gustafson have studied µ 1 (T ) for normal operators on finite and infinite dimensional spaces [9,10,15]. See also Davis [1] and Mirman [12].…”

“…The following two theorems, summarize what we know, as to date, about µ 1 (T ) for normal operators T . See [9,10,14] for their proofs. We will use these results in the following analysis of normal subalgebras.…”

Extending Kantorovich-Type Inequalities to Normal Operators

“…He found some partial and implicit results for (6) when T is an accretive normal matrix on a finite dimensional Hilbert space. In [5] and [6] Gustafson and Seddighin found more explicit results for (6), assuming that T is a normal matrix on a finite dimensional space. They proved that in this case (6) is always expressed by at most two eigenvalues of T. This property that later was generalized by Seddighin as The Two Nonzero Component Lemma (or TNCL for short) was implicitly proved in [5].…”

“…A geometric proof for this lemma in the finite dimensional case is implicit in the proof of Theorem 5.1 in [5]. Using the notations in the Lemma 1 above, in …”