More on Rav Elyashiv ZT"L
From Rav Aviner's English website, talking about Rav Elyashiv:
The True Gaon since he respected every Torah scholar even if there were differences of opinion.
[For example, in his relationship to Maran Ha-Rav Kook. His connection with Ha-Rav Kook already began with his grandfather, Ha-Gaon Ha-Gadol Ha-Mekubal, Ha-Rav Shlomo Eliyashuv, the author of "Leshem Shevo Ve-Achlama," from whom Rav Kook learned. And Rav Eliyashuv great respected his student. He once said: There are different ways in Kabbalah: Ha-Ra'avad and Ha-Ramban, Ha-Ramak and Ha-Ari, Ha-Rama Mi-Pano and Ha-Ramchal, Ha-Gra and others, but Ha-Rav Kook includes all of them, no hidden teaching escapes him.
In the year 5682, Ha-Rav Kook attained permission for Ha-Rav Eliyashuv to make Aliyah, and his grandson, our Rabbi, made Aliyah with him. Rav Eliyashuv and Rav Kook also learned many nights together in Yerushalayim. When zealots spoke against Rav Kook. Ha-Rav Eliyashuv silenced them: You can't tell me who he is. We have spent nights learning together.
R' Aryeh Levin once spoke with Rav Kook about his sorrow that there was a wonderful, righteous, young Torah scholar who would be a great match for his (R' Aryeh's) daughter, but the young man did not respond favorably to his suggestion (either because he thought he had better options or because he was not ready to marry). Rav Kook asked for the identity of the young man, and was told that is was our Rabbi. Maran Ha-Rav called for the young man and spoke to him. The younger Rav Elyashiv then accepted the proposal and the couple married. Rav Kook served as the Mesader Kiddushin. Ha-Rabbanit Sheina Chaya ztz"l shared her husband's respect for Rav Kook, and when she once saw from the window how people were scorning him on the street and trying to knock off his hat, she was incapacitated for months.
It once happened that one of the editors of the "Otzar Mefarshei Ha-Talmud" (Treasury of Talmudic Commentators) refused to include Rav Kook's teaching on the Gemara, and was therefore fired by the chief editor. The editor did not accept his decision, and they went to our Rabbi. Ha-Rav Elyashiv was shocked and said to the editor: "Did you know Ha-Rav Kook?! You should know – he was holy. I would have fired you too." And this happened with other books as well.]
|Rav Elyashiv ZT"L with YBLTV"A Rav Ovadia Yosef Shlit"a and others as Dayanim (Source: Kikar)|
Also, according to this write-up on the life of Rav Ovadia Shlit"a, it was Rav Elyashiv ZT"L who convinced a hesitant Rav Ovadia to be a candidate for the position of Chief Rabbi of Israel.