Basileios I said:
Does it say anything about the nature of the fleet?
That is was the Constantinople fleet headed by a dux Paulus.
Sinking the entire Umayyad fleet (roughly 1000 vessels) is not significant? No .... because the Byzantines did it and not the Arabs. :wacko:
Because it was a purely defensive operation. It didn't change anything. (except that perhaps the Umayyads could have used that fleet to flee from the Abbasids.

)
And the heydey of Arab (African/Spanish) sea projection was after that.
Because he was busy fighting internal rivals (revolt of Bardas Skleros, for example), Arabs and Bulgars. He had more important things to do than care about some minor cities in Italy, etc., etc.
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You're missing the point here. You asserted the navy under Basil II was a mighty, mighty thing, its heyday, etc. What did it do? I've gone through a list of major naval events that happened during his reign. Where was the Byzantine navy? It wasn't defending Byzantine dominions, or ferrying its troops, did not attack pirates or protect shipping, or retaliate against raids, did not take the fight anywhere, in fact it was nowhere to be seen. Instead, we see an Emperor begging & paying huge concessions to foreigners to do all the naval work.
If he had a mighty, mighty navy, it did nothing whatsoever.
My sources claim it was just a commercial treaty with Venice, nothing more.
Your sources are wrong. The 992 treaty was a military agreement in return for commercial privileges. The 1002 & 1004 interventions (& others explicitly invoked that treaty.
That's only one of many treaties. Such treaties were made before and would be made again, each conceding more and more.
The Venetians occupied a few islands off the coast. Dalmatia proper was controled by the Croats, which paid tribute to the Empire.
The parts captured by the Venetians were the major citadels on the Dalmatian coast, the parts that had been formerly suzerain to Byzantium. Croatians took the Slavic-populated rump, lost long ago, and paid little beyond lip service. Basil conceded the title of
Dux Dalmatia to Venice.
Sardinia was de-facto independent anyway.
Indeed. Because the Byzantine navy couldn't project itself there.
Why should they do it themselves when the Venetians were willing to do it? Keep in mind the Byzantine philosophy concerning foreign policy. Paying off or bribing enemies as well as hiring others to do the dirty work was one of the main points in the Byzantine doctrine. That's why they got this (unfounded) reputation of being cowards and decrepit.
The Venetians weren't "willing" to do it, they were "paid" to do it. It
cost the Byzantines territory & treasure. Keep that in mind.
You may call appeasement and concessions a "philosophy". Others call it a sign of weakness. If they had an uber-army and uber-navy, they could have deployed it rather than drain their treasury and surrender their lands?
It does sound decrepit. It sounds like the philosophy of that famous fictional Chinese character,
Ah Q, who mentally tricked himself into believing that every beating he took was a glorious victory (one of the best satires about decrepit empires there is.)
Why on earth should Basil II attack Sardinia and Corsica?
He planned to attack Sicily, but never Sardinia or Corsica.
Because (a) they were Byzantine dominions, (b) they were perches from which the Spaniards dominated the Mediterranean sea and attacked other Byz positions. The Spaniards had no problem projecting themselves to Crete & Greece.
If Byz had a competent navy, retaking the islands would have been paramount to taking back control of the sea. But, as you point out, they didn't even bother to try.
(P.S. - the Byzantine navy had better days before Basil. At least it had tried (but failed) to knock out the Fraxinet perch earlier in the 10th C., and that is even further than Corsica.)
Your logic is working akin to this: I am a mighty, mighty composer, the greatest since Mozart. Unfortunately, nobody ever hears my music because I don't write it. Indeed, I prefer to pay others to write. But I am a mighty, mighty composer. And if I repeat it often enough, others will realize that. Have you seen my fancy baton? It was once owned by Mendelssohn. I have a coat of tails in my closet too. Thus it must be true that I am a mighty, mighty composer.