# Real and Complex Operator Norms

@article{Holtz2005RealAC, title={Real and Complex Operator Norms}, author={Olga Holtz and Michael Karow}, journal={arXiv: Functional Analysis}, year={2005} }

Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators:

## 7 Citations

### Symmetric Grothendieck inequality

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- 2020

An analogue of the Grothendieck inequality where the rectangular matrix is replaced by a symmetric/Hermitian matrix and the bilinear form by a quadratic form is established, which allows to simplify proofs, extend results from real to complex, obtain new bounds or establish sharpness of existing ones.

### Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions

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We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the…

### Integration based solvers for standard and generalized Hermitian eigenvalue problems

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Diese Arbeit beschaftigt sich mit der Berechnung von Eigenwerten und
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### Sharp estimates for conditionally centred moments and for compact operators on $L^p$ spaces

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Let $(\Omega, \mathcal{F}, \mathbf{P})$ be a probability space, $\xi$ be a random variable on $(\Omega, \mathcal{F}, \mathbf{P})$, $\mathcal{G}$ be a sub-$\sigma$-algebra of $\mathcal{F}$, and let…

### Bi-Laplacians on graphs and networks

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We study the differential operator $$A=\frac{d^4}{dx^4}$$ A = d 4 d x 4 acting on a connected network $$\mathcal {G}$$ G along with $$\mathcal L^2$$ L 2 , the square of the discrete Laplacian acting…

### Real and complex operator norms

- Mathematics
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Any bounded linear operator between real (quasi-)Banach spaces T : X ® Y has a natural bounded complex linear extension TC : XC ® YC defined by the formula TC(x+iy)=Tx+iTy for x,yIX, where XC and Y…

## References

SHOWING 1-6 OF 6 REFERENCES

### On Vector‐valued Inequalities of the Marcinkiewicz‐Zygmund, Herz and Krivine Type

- Mathematics
- 1994

Any continuous linear operator T: Lp Lq has a natural vector-valued extension T: Lp(l) Lq(l) which is automatically continuous. Relations between the norms of these operators in the cases of p = q…

### Matrix Perturbation Theory

- Computer Science
- 1991

X is the vector space which acts in the n-dimensional (complex) vector space R.1.1 and is related to Varepsilon by the following inequality.

### Real and Complex Analysis. McGraw-Hill Series in Higher Mathematics

- McGraw-Hill Book Company,
- 1966