Geodesic
Closed sectorial forms and one-parameter contraction semigroups
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 643-654.

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Suppose that $s[u,v]$ is a closed sesquilinear sectorial form with vertex at zero, half-angle$\alpha\in[0,\pi/2)$, and dense domain $\mathscr D(s)$ in a Hilbert space $H$, $S$ is them-sectorial operator associated with $s$, $S_R$ is the real part of $S$, and $T(t)=\exp(-tS)$ is the contraction semigroup with generator $-S$, holomorphic in the sector $|\arg t|\pi/2-\alpha$. We characterizes in terms of $T(t)$. In particular, we prove that the following conditions: 1) $u\in\mathscr D(s)$; 2) the function $\|T(t)u\|$ is differentiable at zero; 3) the function $\bigl(T(t)u,u\bigr)$ is differentiable at zero. 
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Yu. M. Arlinskii. Closed sectorial forms and one-parameter contraction semigroups. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 643-654. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a0/

[1] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | Zbl

[2] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[3] Klement F., Kheimans Kh., Angenent S., van Duin K., de Pakhter B., Odnoparametricheskie polugruppy, Mir, M., 1992

[4] Krein S. G., “Teoriya samosopryazhennykh rasshirenii poluogranichennykh ermitovykh operatorov i ee prilozheniya. I”, Matem. sb., 20(62):3 (1947), 431–495 | MR | Zbl

[5] Shmulyan Yu. L., “Dvustoronnee delenie v koltse operatorov”, Matem. zametki, 1:5 (1967), 605–610 | MR | Zbl

[6] Ando T., Nishio K., “Positive self-adjoint extensions of positive symmetric operators”, Tôhoku Math. J., 22 (1970), 65–75 | DOI | MR | Zbl

[7] Arlinskii Yu. M., “Ob odnom klasse szhatii v gilbertovom prostranstve”, Ukr. matem. zh., 39:6 (1977), 691–696 | MR

[8] Sëkefalvi-Nad B., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970

[9] Fillmore P. A., Williams J. P., “On operator ranges”, Adv. Math., 7 (1971), 254–281 | DOI | MR | Zbl

[10] Shmulyan Yu. L., “O nekotorykh svoistvakh stabilnosti dlya analiticheskikh operator-funktsii”, Matem. zametki, 20:4 (1976), 511–520 | MR | Zbl