Index of notation

The reference numbers indicate the chapter and page (and, occasionally, exercise).

$|\xi|,\ \|x\| :$ I, p. 3. $\mathscr{B}(I;\ K),\ \mathscr{B}_K(I),\ \ell^\infty_K(I),\ \ell^1_K(I),\ \mathscr{B}(I),\ \ell^1(I) :$ I, p. 4. $E_A$ (A a convex symmetric set in a real vector space E) : II, p. 26. $\langle x,\ y \rangle :$ II, p. 42. $\sigma(F,\ G) :$ II, p. 42. $M^\circ,\ M^{\circ\circ} :$ II, p. 44. $^t u$ (u a linear mapping) : II, p. 46. $\mathscr{R}(X) :$ III, p. 9. $\mathscr{C}^\infty(U) :$ III, p. 9. $\mathscr{C}_H^\infty(U),\ \mathscr{C}_0^\infty(U) :$ III, p. 9. $\mathscr{G}_{s,M}(I),\ \mathscr{G}_s(I),\ \mathscr{C}(I) :$ III, p. 10. $\mathscr{H}(U),\ \mathscr{H}(L)$ (U an open subset of $\mathbf{C}^n$, L a compact subset of $\mathbf{C}^n$) : III, p. 10. $\mathscr{L}(E;\ F) :$ III, p. 13. $\mathscr{L}_\varepsilon(E;\ F) :$ III, p. 13. $\mathscr{L}_s(E;\ F),\ \mathscr{L}_c(E;\ F),\ \mathscr{L}_{pc}(E;\ F),\ \mathscr{L}_{cc}(E;\ F),\ \mathscr{L}_b(E;\ F) :$ III, p. 14. $E',\ E'_\varepsilon,\ E'_s,\ E'_c,\ E'_{pc},\ E'_{cc},\ E'_b :$ III, p. 14. $\mathscr{L}(E),\ \mathscr{L}_\varepsilon(E),\ \mathscr{L}_s(E),\ \mathscr{L}_c(E),\ \mathscr{L}_{pc}(E),\ \mathscr{L}_{cc}(E),\ \mathscr{L}_b(E) :$ III, p. 14. $p_M$ (p a semi-norm, M a bounded subset) : III, p. 14. $\mathscr{C}_0(\mathbf{R}) :$ III, p. 18. $\tau(E,\ F) :$ IV, p. 2. $\beta(E,\ F) :$ IV, p. 4. $c_E :$ IV, p. 14. $\ell^\infty(\mathbf{N}) :$ IV, p. 17 $c_0(\mathbf{N}),\ \ell^1(\mathbf{N}) :$ IV, p. 18. $S(E) :$ IV, p. 26. $H_p :$ IV, p. 26. $E_\sigma :$ IV, p. 32. $\mathscr{C}_s(X) :$ IV, p. 33. $\mathscr{C}^b(X),\ \mathscr{C}(X) :$ IV, p. 36. $\mathscr{B}(X;\ \mathbf{R}) :$ IV, p. 40. $\mathrm{Ind}(u)$ (u a Fredholm operator) : IV, p. 66, exerc. 21. $\xi :$ V, p. 1. $\ell^2,\ \ell^2(\mathbf{N}) :$ V, p. 4. $E_{(c)} :$ V, p. 4. $\langle x|y \rangle,\ \|x\| = \langle x|x \rangle^{1/2},\ (x|y) = \langle y|x \rangle :$ V, p. 5. $E$ (E a complex prehilbertian space) : V, p. 6. $\mathscr{H}^s$ (Sobolev space) : V, p. 6. $H^2(D) :$ V, p. 7. $\mathscr{C}_0^1(U) :$ V, p. 8. $p_H$ (H convex separated and complete set in a prehilbertian space) : V, p. 10. $x^*$ (x a vector of a Hilbert space) : V, p. 15 et p. 40. $\bigoplus_{i \in I} E_i :$ V, p. 18. $E_1 \oplus E_2 \oplus \cdots \oplus E_n$ (E_i Hilbert spaces) : V, p. 18. $\ell^2_E(I),\ \ell^2(\hat{I})$ (E a Hilbert space) : V, p. 18.

$E_1 \otimes_2 E_2, \|z\|_2 (z \in E_1 \otimes_2 E_2) :$ V, p. 26. $E_1 \otimes_2 E_2 \otimes_2 \cdots \otimes_2 E_n, \bigotimes_{i=1}^n E_i, \|z\|_2 \left( z \in \bigotimes_{i=1}^n E_i \right) :$ V, p. 27. $E_1 \hat{\otimes}_2 E_2 \hat{\otimes}_2 \cdots \hat{\otimes}_2 E_n, \bigotimes_{1 \leq i \leq n} E_i :$ V, p. 28 $u_1 \hat{\otimes}_2 u_2 \hat{\otimes}_2 \cdots \hat{\otimes}_2 u_n$ (u_i linear mappings) : V, p. 28. $\hat{T}^n(E), E^{\hat{\otimes}_n} :$ V, p. 29. $\hat{S}^n(E), \hat{S}(E) :$ V, p. 30. $\hat{T}^n(u), \hat{S}^n(u)$ (u a linear mapping) : V, p. 31 and p. 32. $\hat{\Lambda}^n(E), \hat{\Lambda}(E) :$ V, p. 33. $\hat{\Lambda}^n(u)$ (u a linear mapping) : V, p. 34. $v.u, vu$ (u, v linear mappings) : V, p. 37. $u^*$ (u a linear mapping) : V, p. 38. $\mathscr{H}(E)$ (E a Hilbert space) : V, p. 44. $u \geq 0$ (u an endomorphism of a Hilbert space) : V, p. 45. $\mathscr{L}_+(E) :$ V, p. 45. $u \geq v$ (u, v in $\mathscr{L}(E)$, E a Hilbert space) : V, p. 45. $\tau(u)$ (u an endomorphism of finite rank) : V, p. 48. $\mathrm{Tr}(u)$ ($u \geq 0$ in $\mathscr{L}(E)$) : V, p. 49. $\mathscr{L}^1(E)$ (E a Hilbert space) : V, p. 51. $\mathscr{L}^2(E; F), \mathscr{L}^2(E)$ (E, F Hilbert spaces) : V, p. 52. $\|u\|_2$ ($u \in \mathscr{L}(E; F)$, E, F Hilbert spaces) : V, p. 52. $\mathrm{Tr}(\mathbf{Q}/H)$ (Q, H positive quadratic forms) : V, p. 57.