We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [operator-theory]

Operator theory is the branch of functional analysis that focuses on bounded linear operators, but it includes closed operators and nonlinear operators. Operator theory is also concerned with the study of algebras of operators.

6,704 questions
Filter by
Sorted by
Tagged with
7 views

28 views

### Normal plus compact is Fredholm with index 0

Let $T, K \in B(H)$, $TT^{*} = T^{*}T$, $K$ compact. Why is $T+K$ Fredholm and $ind(T +K) = 0$? Is it even true? I have forgotten all I knew about Fredholm theory and I need that result for proving ...
21 views

### Comparison of projections in $B(H)$

Suppose $P$, $Q$ are two non-trivial projections in $B(H)$, can we deduce that $P\leq Q$ or $Q\leq P$?
42 views

### Is the point spectrum always countable?

I have this very simple question. Premise: Let $A$ be a linear densely defined symmetric/self-adjoint operator in a complex separable Hilbert space $\mathcal H$ (typical example in Quantum Mechanics)....
34 views

### compute the sprectrum of the sum of orthogonal projections [closed]

Suppose $\{p_i\},i=1,\cdots,n$ are different projections and they are mutually orthogonal in a $C^*$-algebra,how to compute the spectrum $\sigma(k_1p_1+\cdots+k_np_n)$ of $k_1p_1+\cdots+k_np_n$, ...
23 views

18 views

### definition of anti-unitary operator

The definition of anti-unitary operator is given as following: A bounded anti-linear operator $U$ is anti-unitary if $UU^*=U^*U=1$ But I found another definition in Wiki:an anti-unitary operator $U$...
20 views

### difference between continuous functional calculus and borel functional calculus

When $N$ is a normal operator on $H$ with spectral measure $E$,let $B(\sigma(N))$ be the $C^*$ algebra of bounded Borel functions on $\sigma(N)$ ,we have the map $\psi\mapsto \psi(N)$,which is a ...
21 views

### The spectrum of an irreducible reversible Markov kernel is contained in $[-1,1)$
Let $(E,\mathcal E)$ be a measurable space, $\kappa$ be a Markov kernel on $(E,\mathcal E)$, $\mu$ be a probability measure on $(E,\mathcal E)$ reversible with respect to $\kappa$ and L^2_0(\mu):=\...