Questions tagged [unbounded-operators]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
16 votes
2 answers
937 views

Perturbation of unbounded self-adjoint operators

In the paper "A CRITERION FOR THE NORMALITY OF UNBOUNDED OPERATORS AND APPLICATIONS TO SELF-ADJOINTNESS" by M. H MORTAD (http://arxiv.org/pdf/1301.0241.pdf), the author states the following theorem ...
m.gn's user avatar
  • 163
11 votes
3 answers
433 views

Does the generator of a 1-parameter group of Banach space isometries know which elements are entire?

Let $X$ be a complex Banach space. Let $(\sigma_t)_{t \in \mathbb{R}}$ be a 1-parameter group of linear isometries of $X$ which is strongly continuous i.e. $t \mapsto \sigma_t(x)$ is continuous for ...
Michael's user avatar
  • 672
8 votes
1 answer
641 views

When is the adjoint of a hypoelliptic operator also hypoelliptic?

Suppose that $M$ is a smooth manifold with a measure $\mu$ and let $L^2(M, \mu)$ be a space of all square-integrable functions on $M$. Recall that $L$ is a hypoelliptic differential operator if for ...
vkrouglov's user avatar
  • 329
5 votes
1 answer
2k views

Commuting with self-adjoint operator

Let $T$ be an (unbounded) self-adjoint operator. Assume that there is a bounded operator $S$ such that $TS=ST.$ For which kind of $f$ do we have that $f(T)S=Sf(T)?$ My thought was that using a ...
Zinkin's user avatar
  • 491
4 votes
0 answers
2k views

Product of positive commuting operators

Let $A$ and $B$ be positive commuting bounded operators on a Hilbert space. It can be shown by functional calculus that $AB=A^{1/2}BA^{1/2},$ so that $AB$ is again positive. If $A$ and $B$ are not ...
yurius's user avatar
  • 541
4 votes
1 answer
751 views

Commuting with an unbounded operator

Let $H$ be a Hilbert space. Let $A$ be a closed unbounded operator, and let $B\in B(H)$ be a bounded operator. Definition:   $A$ and $B$ strong-commute if the partial isometry in the polar ...
André Henriques's user avatar
3 votes
2 answers
217 views

Question about the Bessel operator

For $\nu>-1$ denote by $\{\lambda_{k,\nu}\}_{k\in\mathbb{N}}$ the succesive positive zeros of the Bessel function of the first kind $J_{\nu}$. The Bessel operator is given by \begin{equation*} L_\...
Tony419's user avatar
  • 401
2 votes
1 answer
209 views

If $A$ is a closed operator, is $A^k$ closed?

Let $A$ be a closed (densely defined) operator on a Hilbert space $H$. We define for a natural number $k$, the operator $A^k$ with its natural domain. Is $A^k$ closed?
Andromeda's user avatar
  • 189