query: Can a self-adjoint operator in a C*-algebra be such that $\|a^3\|\neq \|a\|^3$?
positive_passages.docid: 158082
positive_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 54294
negative_passages.text: Can the product $AB$ be computed using only $+, -,$ and reciprocal operators?
negative_passages.docid: 32606
negative_passages.text: Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
negative_passages.docid: 54099
negative_passages.text: What are the eigenvalues of $\operatorname{ad}x$?
negative_passages.docid: 128917
negative_passages.text: Inner Product on $\mathbb{R}$ and on $\mathbb{C}$
negative_passages.docid: 121802
negative_passages.text: Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
negative_passages.docid: 150287
negative_passages.text: Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
negative_passages.docid: 124003
negative_passages.text: Composition of adjoint functors
negative_passages.docid: 71011
negative_passages.text: Criteria of compactness of an operator
negative_passages.docid: 41013
negative_passages.text: Subspace of $C^3$ that spanned by a set over C and over R
negative_passages.docid: 55787
negative_passages.text: Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$?
negative_passages.docid: 90757
negative_passages.text: $T$ self-adjoint on Hilbert space $H$, $T^n=T^{n+1}$ will $T$ be an orthogonal projection operator?
negative_passages.docid: 95481
negative_passages.text: The set of self-adjoint operators over a Hilbert space doesn't form a lattice
negative_passages.docid: 119352
negative_passages.text: compact and self adjoint square root of an operator
negative_passages.docid: 93062
negative_passages.text: Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?
negative_passages.docid: 53634
negative_passages.text: Sequences or 'chains' of adjoint functors
negative_passages.docid: 117688
negative_passages.text: Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$